Friday, August 18, 2017

Number of the day: 4603

Properties of the number 4603:

4603 is a cyclic number.
4603 is the 623th prime.
4603 has 21 antidivisors and 4602 totatives.
4603 has an emirp digit sum 13 in base 10.
4603 has a Fibonacci digit sum 13 in base 10.
4603 = 23022 - 23012 is the difference of 2 nonnegative squares in 1 way.
4603 is the sum of 2 positive triangular numbers.
4603 is the difference of 2 positive pentagonal numbers in 1 way.
4603 = 32 + 252 + 632 is the sum of 3 positive squares.
46032 is the sum of 3 positive squares.
4603 is a proper divisor of 1793 - 1.
4603 is an emirp in (at least) the following bases: 4, 13, 17, 19, 22, 24, 29, 33, 35, 37, 38, 49, 50, 51, 55, 65, 67, 71, 75, 77, 78, 81, 83, 86, 93, 95, and 96.
4603 is palindromic in (at least) the following bases: 43, 59, -40, -46, and -78.
4603 in base 17 = ffd and consists of only the digits 'd' and 'f'.
4603 in base 39 = 311 and consists of only the digits '1' and '3'.
4603 in base 42 = 2PP and consists of only the digits '2' and 'P'.
4603 in base 43 = 2L2 and consists of only the digits '2' and 'L'.
4603 in base 58 = 1LL and consists of only the digits '1' and 'L'.
4603 in base 59 = 1J1 and consists of only the digits '1' and 'J'.

The number 4603 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031936: Lower prime of a difference of 18 between consecutive primes.
A056108: Fourth spoke of a hexagonal spiral.
A066540: The first of two consecutive primes with equal digital sums.
A095673: Primes p = p_(n+1) such that p_n + p_(n+2) = 2*p_(n+1) + 12.
A100201: Primes of the form 23n+3.
A104824: Primes from merging of 4 successive digits in decimal expansion of Pi.
A113743: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, ..., 1.
A198164: Primes from merging of 4 successive digits in decimal expansion of sqrt(2).
A272160: Primes of the form abs(8n^2 - 488n + 7243) in order of increasing nonnegative values of n.
A275183: T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.

Thursday, August 17, 2017

Number of the day: 412485

Pierre de Fermat was born on this day 416 years ago.

Properties of the number 412485:

412485 is a cyclic number.
412485 = 3 × 5 × 107 × 257 is the 377675th composite number and is squarefree.
412485 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 217088 totatives.
Reversing the decimal digits of 412485 results in a sphenic number.
412485 = 2062432 - 2062422 = 687492 - 687462 = 412512 - 412462 = 137572 - 137422 = 19812 - 18742 = 9312 - 6742 = 8032 - 4822 = 6532 - 1182 is the difference of 2 nonnegative squares in 8 ways.
412485 is the difference of 2 positive pentagonal numbers in 3 ways.
412485 = 202 + 712 + 6382 is the sum of 3 positive squares.
4124852 = 2044772 + 3582362 = 513602 + 4092752 = 2866532 + 2966042 = 2474912 + 3299882 is the sum of 2 positive squares in 4 ways.
4124852 is the sum of 3 positive squares.
412485 is a proper divisor of 64316 - 1.
412485 is palindromic in (at least) base -92.

Wednesday, August 16, 2017

Number of the day: 229585

Arthur Cayley was born on this day 196 years ago.

Properties of the number 229585:

229585 is a cyclic number.
229585 = 5 × 17 × 37 × 73 is the 209187th composite number and is squarefree.
229585 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 165888 totatives.
229585 has an emirp digit sum 31 in base 10.
229585 = 1147932 - 1147922 = 229612 - 229562 = 67612 - 67442 = 31212 - 30842 = 16092 - 15362 = 13932 - 13082 = 7132 - 5282 = 4972 - 1322 is the difference of 2 nonnegative squares in 8 ways.
229585 is the sum of 2 positive triangular numbers.
229585 is the difference of 2 positive pentagonal numbers in 7 ways.
229585 = 2972 + 3762 = 1592 + 4522 = 2362 + 4172 = 882 + 4712 = 3242 + 3532 = 1922 + 4392 = 1442 + 4572 = 122 + 4792 is the sum of 2 positive squares in 8 ways.
229585 = 32 + 702 + 4742 is the sum of 3 positive squares.
2295852 = 1565852 + 1679002 = 1080402 + 2025752 = 365002 + 2266652 = 1467752 + 1765402 = 815852 + 2146002 = 75752 + 2294602 = 1215402 + 1947752 = 518002 + 2236652 = 235402 + 2283752 = 1478522 + 1756392 = 1181932 + 1968242 = 828962 + 2140972 = 1067992 + 2032322 = 351132 + 2268842 = 403692 + 2260082 = 1437362 + 1790232 = 1227292 + 1940282 = 531672 + 2233442 = 1594322 + 1651992 = 972362 + 2079772 = 245282 + 2282712 = 1558572 + 1685762 = 927592 + 2100122 = 196332 + 2287442 = 1316162 + 1881132 = 634922 + 2206312 = 114962 + 2292972 = 1377512 + 1836682 = 1290642 + 1898732 = 707372 + 2184162 = 1180482 + 1969112 = 478042 + 2245532 = 276082 + 2279192 = 903212 + 2110722 = 169832 + 2289562 = 581912 + 2220882 = 1509602 + 1729752 = 1146652 + 1989002 = 867002 + 2125852 = 744602 + 2171752 is the sum of 2 positive squares in 40 ways.
2295852 is the sum of 3 positive squares.
229585 is a proper divisor of 15118 - 1.

The number 229585 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A218135: Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
A255214: Number of partitions of n^2 into at most 10 square parts.

Tuesday, August 15, 2017

Number of the day: 719628

Happy Pythagorean Theorem Day!

Properties of the number 719628:

719628 = 22 × 3 × 7 × 13 × 659 is the 661629th composite number and is not squarefree.
719628 has 5 distinct prime factors, 48 divisors, 19 antidivisors and 189504 totatives.
719628 has a semiprime digit sum 33 in base 10.
719628 = 1799082 - 1799062 = 599722 - 599662 = 257082 - 256942 = 138522 - 138262 = 85882 - 85462 = 46522 - 45742 = 20682 - 18862 = 9322 - 3862 is the difference of 2 nonnegative squares in 8 ways.
719628 is the difference of 2 positive pentagonal numbers in 3 ways.
719628 = 1062 + 2142 + 8142 is the sum of 3 positive squares.
7196282 = 2767802 + 6642722 is the sum of 2 positive squares in 1 way.
7196282 is the sum of 3 positive squares.
719628 is a proper divisor of 131912 - 1.

The number 719628 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A241576: Third differences of A001521.
A244020: Number of new points at the n-th step of the following iteration, starting with four points in general position in the real projective plane: dualize the current pointset to a family of lines, take all intersections of those lines, repeat.

Monday, August 14, 2017

Number of the day: 749736

Properties of the number 749736:

749736 = 23 × 34 × 13 × 89 is the 689518th composite number and is not squarefree.
749736 has 4 distinct prime factors, 80 divisors, 21 antidivisors and 228096 totatives.
749736 has a triangular digit sum 36 in base 10.
749736 is the difference of 2 nonnegative squares in 20 ways.
749736 is the sum of 2 positive triangular numbers.
749736 is the difference of 2 positive pentagonal numbers in 1 way.
749736 = 5942 + 6302 = 3062 + 8102 is the sum of 2 positive squares in 2 ways.
749736 = 562 + 1942 + 8422 is the sum of 3 positive squares.
7497362 = 3285362 + 6739202 = 440642 + 7484402 = 4957202 + 5624642 = 2883602 + 6920642 is the sum of 2 positive squares in 4 ways.
7497362 is the sum of 3 positive squares.
749736 is a proper divisor of 17918 - 1.
749736 in base 34 = j2j2 and consists of only the digits '2' and 'j'.
749736 in base 35 = hh11 and consists of only the digits '1' and 'h'.

The number 749736 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A157377: a(n) = 531441*n - 313146.

Sunday, August 13, 2017

Number of the day: 4548893344

Properties of the number 4548893344:

4548893344 = 25 × 1889 × 75253 is the 4334179637th composite number and is not squarefree.
4548893344 has 3 distinct prime factors, 24 divisors, 15 antidivisors and 2273212416 totatives.
Reversing the decimal digits of 4548893344 results in a sphenic number.
4548893344 = 11372233372 - 11372233352 = 5686116702 - 5686116662 = 2843058382 - 2843058302 = 1421529252 - 1421529092 = 6039132 - 6001352 = 3047902 - 2972342 = 1580622 - 1429502 = 903652 - 601412 is the difference of 2 nonnegative squares in 8 ways.
4548893344 is the sum of 2 positive triangular numbers.
4548893344 is the difference of 2 positive pentagonal numbers in 2 ways.
4548893344 = 419802 + 527882 = 64122 + 671402 is the sum of 2 positive squares in 2 ways.
4548893344 = 9602 + 28122 + 673802 is the sum of 3 positive squares.
45488933442 = 31570138562 + 32750105602 = 10242525442 + 44320804802 = 8610033602 + 44666658562 = 24800605442 + 38133620802 is the sum of 2 positive squares in 4 ways.
45488933442 is the sum of 3 positive squares.
4548893344 is a proper divisor of 33150168 - 1.

Saturday, August 12, 2017

Number of the day: 58483

Properties of the number 58483:

58483 is a cyclic number.
58483 = 233 × 251 is semiprime and squarefree.
58483 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 58000 totatives.
58483 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 58483 results in a sphenic number.
58483 = 292422 - 292412 = 2422 - 92 is the difference of 2 nonnegative squares in 2 ways.
58483 is the difference of 2 positive pentagonal numbers in 1 way.
58483 = 172 + 872 + 2252 is the sum of 3 positive squares.
584832 = 263552 + 522082 is the sum of 2 positive squares in 1 way.
584832 is the sum of 3 positive squares.
58483 is a proper divisor of 50329 - 1.
58483 is an emirpimes in (at least) the following bases: 5, 6, 8, 11, 14, 15, 16, 17, 20, 22, 25, 26, 27, 29, 33, 34, 38, 39, 41, 43, 46, 48, 50, 51, 54, 55, 56, 58, 59, 61, 64, 70, 72, 75, 76, 77, 81, 86, 87, 91, 92, and 99.
58483 is palindromic in (at least) the following bases: 45, 73, and -56.
58483 in base 45 = SdS and consists of only the digits 'S' and 'd'.
58483 in base 55 = JII and consists of only the digits 'I' and 'J'.

The number 58483 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058518: Number of forests of B-trees of order 3 with n labeled leaves.
A069969: Numbers n such that phi(reverse(n)) = phi(reverse(n-1)) + phi(reverse(n-2)).
A249109: Composite numbers whose sum of aliquot parts divides the sum of the aliquot parts of the numbers less than or equal to n and not relatively prime to n.
A275251: Sequence of pairwise relatively prime numbers of class P_6 (see comment in A275246).

Friday, August 11, 2017

Number of the day: 717853

Properties of the number 717853:

717853 = 233 × 59 is the 659972th composite number and is not squarefree.
717853 has 2 distinct prime factors, 8 divisors, 31 antidivisors and 675004 totatives.
717853 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 717853 results in a semiprime.
717853 = 3589272 - 3589262 = 156172 - 155942 = 61132 - 60542 = 9432 - 4142 is the difference of 2 nonnegative squares in 4 ways.
717853 is the difference of 2 positive pentagonal numbers in 4 ways.
717853 = 292 + 362 + 8462 is the sum of 3 positive squares.
7178532 is the sum of 3 positive squares.
717853 is a proper divisor of 8271058 - 1.
717853 = '71' + '7853' is the concatenation of 2 prime numbers.

The number 717853 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A229146: n^3*(5*n+3)/2.

Thursday, August 10, 2017

Number of the day: 971

Properties of the number 971:

971 is a cyclic number.
971 is the 164th prime.
971 has 5 antidivisors and 970 totatives.
971 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 971 results in an emirp.
971 = 4862 - 4852 is the difference of 2 nonnegative squares in 1 way.
971 is the difference of 2 positive pentagonal numbers in 1 way.
971 = 12 + 32 + 312 is the sum of 3 positive squares.
9712 is the sum of 3 positive squares.
971 is a proper divisor of 23910 - 1.
971 is an emirp in (at least) the following bases: 3, 4, 7, 8, 10, 15, 16, 17, 23, 25, 33, 35, 37, 38, 41, 42, 43, 46, 49, 50, 53, 54, 55, 57, 59, 62, 64, 69, 70, 73, 77, 81, 82, 86, 87, 89, 93, 97, 98, and 100.
971 is palindromic in (at least) the following bases: 19, -14, and -97.
971 in base 7 = 2555 and consists of only the digits '2' and '5'.
971 in base 13 = 599 and consists of only the digits '5' and '9'.
971 in base 15 = 44b and consists of only the digits '4' and 'b'.
971 in base 18 = 2hh and consists of only the digits '2' and 'h'.
971 in base 19 = 2d2 and consists of only the digits '2' and 'd'.

The number 971 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000928: Irregular primes: p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.
A001913: Full reptend primes: primes with primitive root 10.
A005846: Primes of the form n^2 + n + 41.
A006567: Emirps (primes whose reversal is a different prime).
A007500: Primes whose reversal in base 10 is also prime (called "palindromic primes" by D. Wells, although that name usually refers to A002385). Also called reversible primes.
A030430: Primes of the form 10*n+1.
A046132: Larger member p+4 of cousin primes (p, p+4).
A061955: Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 2 (most significant digit on right).
A141111: Primes of the form 4*x^2+x*y-4*y^2 (as well as of the form 4*x^2+9*x*y+y^2).
A235266: Primes whose base 2 representation is also the base 3 representation of a prime.

Wednesday, August 9, 2017

Number of the day: 3505

Properties of the number 3505:

3505 = 5 × 701 is semiprime and squarefree.
3505 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 2800 totatives.
3505 has an emirp digit sum 13 in base 10.
3505 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 3505 results in an emirpimes.
3505 = 142 + … + 232 is the sum of at least 2 consecutive positive squares in 1 way.
3505 = 17532 - 17522 = 3532 - 3482 is the difference of 2 nonnegative squares in 2 ways.
3505 is the difference of 2 positive pentagonal numbers in 2 ways.
3505 = 362 + 472 = 162 + 572 is the sum of 2 positive squares in 2 ways.
3505 = 242 + 252 + 482 is the sum of 3 positive squares.
35052 = 21032 + 28042 = 18242 + 29932 = 9132 + 33842 = 13002 + 32552 is the sum of 2 positive squares in 4 ways.
35052 is the sum of 3 positive squares.
3505 is a proper divisor of 9115 - 1.
3505 is an emirpimes in (at least) the following bases: 4, 7, 10, 12, 13, 15, 16, 17, 18, 23, 26, 27, 29, 31, 37, 38, 39, 42, 45, 50, 51, 57, 61, 62, 65, 66, 68, 69, 71, 73, 74, 75, 79, 84, 87, 88, 89, 91, 92, 93, and 100.
3505 is palindromic in (at least) the following bases: 19, 22, 25, 34, 48, -8, -28, and -73.
3505 in base 8 = 6661 and consists of only the digits '1' and '6'.
3505 in base 19 = 9d9 and consists of only the digits '9' and 'd'.
3505 in base 21 = 7jj and consists of only the digits '7' and 'j'.
3505 in base 22 = 757 and consists of only the digits '5' and '7'.
3505 in base 25 = 5f5 and consists of only the digits '5' and 'f'.
3505 in base 29 = 44p and consists of only the digits '4' and 'p'.
3505 in base 33 = 377 and consists of only the digits '3' and '7'.
3505 in base 34 = 313 and consists of only the digits '1' and '3'.
3505 in base 47 = 1RR and consists of only the digits '1' and 'R'.
3505 in base 48 = 1P1 and consists of only the digits '1' and 'P'.

The number 3505 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006367: Number of binary vectors of length n+1 beginning with 0 and containing just 1 singleton.
A013979: Expansion of 1/(1 - x^2 - x^3 - x^4) = 1/((1 + x)*(1 - x - x^3)).
A026905: Partial sums of the partition numbers A000041.
A072573: Odd interprimes not divisible by 3.
A098237: Composite de Polignac numbers (A006285).
A107458: G.f.: (1-x^2-x^3)/( (1+x)(1-x-x^3) ).
A136392: 6n^2 - 10n + 5.
A182840: Toothpick sequence on hexagonal net.
A205477: L.g.f.: Sum_{n>=1} (x^n/n) * Product_{d|n} (1 + n*x^d/d).
A248112: Number T(n,k) of subsets of {1,...,n} containing n and having at least one set partition into k blocks with equal element sum; triangle T(n,k), n>=1, 1<=k<=floor((n+1)/2), read by rows.

Tuesday, August 8, 2017

Number of the day: 82545

Properties of the number 82545:

82545 = 3 × 5 × 5503 is a sphenic number and squarefree.
82545 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 44016 totatives.
82545 = 412732 - 412722 = 137592 - 137562 = 82572 - 82522 = 27592 - 27442 is the difference of 2 nonnegative squares in 4 ways.
82545 is the difference of 2 positive pentagonal numbers in 2 ways.
82545 = 172 + 402 + 2842 is the sum of 3 positive squares.
825452 = 495272 + 660362 is the sum of 2 positive squares in 1 way.
825452 is the sum of 3 positive squares.
82545 is a proper divisor of 9296 - 1.
82545 = '82' + '545' is the concatenation of 2 semiprime numbers.
82545 in base 14 = 22121 and consists of only the digits '1' and '2'.

The number 82545 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A255550: Main diagonal of array A255551.

Monday, August 7, 2017

Number of the day: 45171

Properties of the number 45171:

45171 = 33 × 7 × 239 is the 40482th composite number and is not squarefree.
45171 has 3 distinct prime factors, 16 divisors, 23 antidivisors and 25704 totatives.
45171 = 225862 - 225852 = 75302 - 75272 = 32302 - 32232 = 25142 - 25052 = 10862 - 10652 = 8502 - 8232 = 3902 - 3272 = 2142 - 252 is the difference of 2 nonnegative squares in 8 ways.
45171 is the sum of 2 positive triangular numbers.
45171 is the difference of 2 positive pentagonal numbers in 1 way.
45171 = 112 + 792 + 1972 is the sum of 3 positive squares.
451712 is the sum of 3 positive squares.
45171 is a proper divisor of 75717 - 1.
45171 = '45' + '171' is the concatenation of 2 triangular numbers.
45171 in base 42 = PPL and consists of only the digits 'L' and 'P'.

The number 45171 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031795: Period of continued fraction for sqrt(n) contains exactly 27 ones.
A050833: Numbers n such that 163*2^n-1 is a prime.
A095053: Number of primes with number of 1-bits equal to one plus number 0-bits (A095073) in range ]2^2n,2^(2n+1)].
A151350: Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, -1), (1, 1)}
A188381: Negabinary Keith numbers.
A241639: Number of partitions p of n such that (number of even numbers in p) >= (number of odd numbers in p).

Sunday, August 6, 2017

Number of the day: 995361

Johann Bernoulli was born on this day 350 years ago.

Properties of the number 995361:

995361 = 3 × 257 × 1291 is a sphenic number and squarefree.
995361 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 660480 totatives.
995361 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 995361 results in a sphenic number.
995361 = 4976812 - 4976802 = 1658952 - 1658922 = 20652 - 18082 = 10312 - 2602 is the difference of 2 nonnegative squares in 4 ways.
995361 is the sum of 2 positive triangular numbers.
995361 is the difference of 2 positive pentagonal numbers in 2 ways.
995361 = 802 + 1692 + 9802 is the sum of 3 positive squares.
9953612 = 1239362 + 9876152 is the sum of 2 positive squares in 1 way.
9953612 is the sum of 3 positive squares.
995361 is a proper divisor of 154315 - 1.
995361 = '995' + '361' is the concatenation of 2 semiprime numbers.

Saturday, August 5, 2017

Number of the day: 677201

Niels Henrik Abel was born on this day 215 years ago.

Properties of the number 677201:

677201 is a cyclic number.
677201 = 7 × 89 × 1087 is a sphenic number and squarefree.
677201 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 573408 totatives.
677201 has a prime digit sum 23 in base 10.
677201 = 3386012 - 3386002 = 483752 - 483682 = 38492 - 37602 = 8552 - 2322 is the difference of 2 nonnegative squares in 4 ways.
677201 is the difference of 2 positive pentagonal numbers in 4 ways.
677201 = 242 + 652 + 8202 is the sum of 3 positive squares.
6772012 = 2967512 + 6087202 is the sum of 2 positive squares in 1 way.
6772012 is the sum of 3 positive squares.
677201 is a proper divisor of 257132 - 1.
677201 is palindromic in (at least) base -40.

Friday, August 4, 2017

Number of the day: 3119

William Rowan Hamilton was born on this day 212 years ago.

John Venn was born on this day 183 years ago.

Properties of the number 3119:

3119 is a cyclic number.
3119 and 3121 form a twin prime pair.
3119 has 21 antidivisors and 3118 totatives.
3119 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 3119 results in a semiprime.
3119 = 15602 - 15592 is the difference of 2 nonnegative squares in 1 way.
3119 is the difference of 2 positive pentagonal numbers in 1 way.
3119 is not the sum of 3 positive squares.
31192 is the sum of 3 positive squares.
3119 is a proper divisor of 21559 - 1.
3119 = '31' + '19' is the concatenation of 2 prime numbers.
3119 is an emirp in (at least) the following bases: 2, 5, 15, 17, 19, 20, 24, 25, 27, 39, 42, 44, 46, 47, 51, 56, 58, 59, 68, 71, 72, 73, 76, 79, 81, 83, 85, 87, 88, 91, 92, 95, 97, and 100.
3119 is palindromic in (at least) the following bases: -15, and -38.
3119 in base 5 = 44434 and consists of only the digits '3' and '4'.
3119 in base 55 = 11d and consists of only the digits '1' and 'd'.

The number 3119 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001126: Primes with 7 as smallest primitive root.
A001154: Describe the previous term! (method A - initial term is 9).
A024770: Right-truncatable primes: every prefix is prime.
A045709: Primes with first digit 3.
A059452: Safe primes (A005385) which are not Sophie Germain primes.
A060229: Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.
A068652: Numbers such that every cyclic permutation is a prime.
A142463: a(n) = 2*n^2 + 2*n - 1.
A164288: Members of A164368 which are not Ramanujan primes.
A215419: Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

Thursday, August 3, 2017

Number of the day: 960

Properties of the number 960:

960 = 26 × 3 × 5 is the 797th composite number and is not squarefree.
960 has 3 distinct prime factors, 28 divisors, 7 antidivisors and 256 totatives.
960 has an emirpimes digit sum 15 in base 10.
960 has a triangular digit sum 15 in base 10.
960 = 62 + … + 142 is the sum of at least 2 consecutive positive squares in 1 way.
960 is the difference of 2 nonnegative squares in 10 ways.
960 is the difference of 2 positive pentagonal numbers in 1 way.
960 is not the sum of 3 positive squares.
9602 = 5762 + 7682 is the sum of 2 positive squares in 1 way.
9602 is the sum of 3 positive squares.
960 is a proper divisor of 312 - 1.
960 is palindromic in (at least) the following bases: 31, 39, 47, 59, 63, 79, and 95.
960 in base 4 = 33000 and consists of only the digits '0' and '3'.
960 in base 15 = 440 and consists of only the digits '0' and '4'.

The number 960 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000118: Number of ways of writing n as a sum of 4 squares; also theta series of lattice Z^4.
A002093: Highly abundant numbers: numbers n such that sigma(n) > sigma(m) for all m < n.
A002417: 4-dimensional figurate numbers: a(n) = n*binomial(n+2, 3).
A005179: Smallest number with exactly n divisors.
A005563: a(n) = n*(n+2) (or, (n+1)^2 - 1).
A025487: List giving least integer of each prime signature; also products of primorial numbers A002110.
A029470: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 25 (most significant digit on left).
A033996: 8 times triangular numbers: a(n) = 4n(n+1).
A051682: 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2.
A075928: List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.

Tuesday, August 1, 2017

Number of the day: 73457

Properties of the number 73457:

73457 is a cyclic number.
73457 = 17 × 29 × 149 is a sphenic number and squarefree.
73457 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 66304 totatives.
73457 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 73457 results in a prime.
73457 = (48 × 49)/2 + … + (81 × 82)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
73457 = 367292 - 367282 = 21692 - 21522 = 12812 - 12522 = 3212 - 1722 is the difference of 2 nonnegative squares in 4 ways.
73457 is the difference of 2 positive pentagonal numbers in 4 ways.
73457 = 892 + 2562 = 42 + 2712 = 1842 + 1992 = 1242 + 2412 is the sum of 2 positive squares in 4 ways.
73457 = 142 + 192 + 2702 is the sum of 3 positive squares.
734572 = 345682 + 648152 = 102952 + 727322 = 490682 + 546652 = 230952 + 697322 = 21682 + 734252 = 455682 + 576152 = 196682 + 707752 = 57452 + 732322 = 427052 + 597682 = 506602 + 531932 = 293932 + 673202 = 326402 + 658072 = 251432 + 690202 is the sum of 2 positive squares in 13 ways.
734572 is the sum of 3 positive squares.
73457 is a proper divisor of 70128 - 1.
73457 = '7' + '3457' is the concatenation of 2 prime numbers.
73457 = '734' + '57' is the concatenation of 2 semiprime numbers.
73457 is palindromic in (at least) the following bases: 2, and 42.
73457 in base 42 = fQf and consists of only the digits 'Q' and 'f'.
73457 in base 56 = NNf and consists of only the digits 'N' and 'f'.

The number 73457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A090508: Least number beginning with prime(n) such that every concatenation is a prime.
A253131: Number of length 3+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero

Monday, July 31, 2017

Number of the day: 741593

Properties of the number 741593:

741593 is a cyclic number.
741593 is the 59644th prime.
741593 has 31 antidivisors and 741592 totatives.
741593 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 741593 results in an emirp.
741593 = 543 + 583 + 733 is the sum of 3 positive cubes in 1 way.
741593 = 3707972 - 3707962 is the difference of 2 nonnegative squares in 1 way.
741593 is the sum of 2 positive triangular numbers.
741593 is the difference of 2 positive pentagonal numbers in 1 way.
741593 = 4522 + 7332 is the sum of 2 positive squares in 1 way.
741593 = 122 + 432 + 8602 is the sum of 3 positive squares.
7415932 = 3329852 + 6626322 is the sum of 2 positive squares in 1 way.
7415932 is the sum of 3 positive squares.
741593 is a proper divisor of 4792699 - 1.
741593 = '7' + '41593' is the concatenation of 2 prime numbers.
741593 = '7415' + '93' is the concatenation of 2 semiprime numbers.
741593 is an emirp in (at least) the following bases: 7, 10, 18, 26, 28, 40, 49, 55, 57, 76, 84, 85, 88, 93, and 94.

Sunday, July 30, 2017

Number of the day: 88655022

Properties of the number 88655022:

88655022 = 2 × 32 × 421 × 11699 is the 83511370th composite number and is not squarefree.
88655022 has 4 distinct prime factors, 24 divisors, 41 antidivisors and 29478960 totatives.
88655022 has a triangular digit sum 36 in base 10.
88655022 is the sum of 2 positive triangular numbers.
88655022 is the difference of 2 positive pentagonal numbers in 3 ways.
88655022 = 3382 + 4872 + 93972 is the sum of 3 positive squares.
886550222 = 61068782 + 884444402 is the sum of 2 positive squares in 1 way.
886550222 is the sum of 3 positive squares.
88655022 is a proper divisor of 166317547 - 1.

Saturday, July 29, 2017

Number of the day: 4604

Properties of the number 4604:

4604 = 22 × 1151 is the 3980th composite number and is not squarefree.
4604 has 2 distinct prime factors, 6 divisors, 15 antidivisors and 2300 totatives.
4604 has a semiprime digit sum 14 in base 10.
4604 = 11522 - 11502 is the difference of 2 nonnegative squares in 1 way.
4604 is the difference of 2 positive pentagonal numbers in 1 way.
4604 is not the sum of 3 positive squares.
46042 is the sum of 3 positive squares.
4604 is a proper divisor of 68310 - 1.
4604 is palindromic in (at least) the following bases: 18, -43, and -59.
4604 in base 17 = ffe and consists of only the digits 'e' and 'f'.
4604 in base 18 = e3e and consists of only the digits '3' and 'e'.

The number 4604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004112: Numbers n where |cos(n)| (or |cosec(n)| or |cot(n)|) decreases monotonically to 0; also |tan(n)|, |sec(n)|, |sin(n)| increases.
A046964: Sin(n) decreases monotonically to -1.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A065850: Let u be any string of n digits from {0,...,8}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u; then a(n) = max_u f(u).
A066857: Smallest number k such that n! - k is a square
A085329: Non-palindromic solutions to sigma(Rev(n)) = sigma(n).
A139479: Numbers n such that 24n+7 belongs to A000043.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A220681: T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links
A237834: Number of partitions of n such that (greatest part) - (least part) >= number of parts.

Thursday, July 27, 2017

Number of the day: 9842

Properties of the number 9842:

9842 = 2 × 7 × 19 × 37 is the 8627th composite number and is squarefree.
9842 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 3888 totatives.
9842 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 9842 results in a semiprime.
9842 = 42 + 52 + 992 is the sum of 3 positive squares.
98422 = 31922 + 93102 is the sum of 2 positive squares in 1 way.
98422 is the sum of 3 positive squares.
9842 is a proper divisor of 15974 - 1.
9842 = '9' + '842' is the concatenation of 2 semiprime numbers.
9842 is palindromic in (at least) the following bases: 26, 29, 60, -3, -27, -80, and -82.
9842 in base 3 = 111111112 and consists of only the digits '1' and '2'.
9842 in base 24 = h22 and consists of only the digits '2' and 'h'.
9842 in base 26 = eee and consists of only the digit 'e'.
9842 in base 27 = dde and consists of only the digits 'd' and 'e'.
9842 in base 29 = bkb and consists of only the digits 'b' and 'k'.
9842 in base 37 = 770 and consists of only the digits '0' and '7'.
9842 in base 40 = 662 and consists of only the digits '2' and '6'.
9842 in base 49 = 44g and consists of only the digits '4' and 'g'.
9842 in base 59 = 2mm and consists of only the digits '2' and 'm'.
9842 in base 60 = 2i2 and consists of only the digits '2' and 'i'.

The number 9842 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A007051: a(n) = (3^n + 1)/2.
A047848: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
A059934: Third step in Goodstein sequences, i.e. g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5).
A124302: Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
A191450: Dispersion of (3n-1), read by antidiagonals.
A243066: Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
A243506: Permutation of natural numbers: a(n) = A048673(A122111(n)).
A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
A278984: Array read by antidiagonals downwards: T(b,n) = number of words of length n over an alphabet of size b that are in standard order.

Wednesday, July 26, 2017

Number of the day: 81140298

Properties of the number 81140298:

81140298 = 2 × 3 × 19 × 711757 is the 76408061th composite number and is squarefree.
81140298 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 25623216 totatives.
81140298 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 81140298 results in a sphenic number.
81140298 = 953 + 3083 + 3713 is the sum of 3 positive cubes in 1 way.
81140298 = 322 + 1152 + 90072 is the sum of 3 positive squares.
811402982 = 209036102 + 784014482 is the sum of 2 positive squares in 1 way.
811402982 is the sum of 3 positive squares.
81140298 is a proper divisor of 12914652 - 1.

Tuesday, July 25, 2017

Number of the day: 10956

Properties of the number 10956:

10956 = 22 × 3 × 11 × 83 is the 9625th composite number and is not squarefree.
10956 has 4 distinct prime factors, 24 divisors, 9 antidivisors and 3280 totatives.
10956 has a semiprime digit sum 21 in base 10.
10956 has a Fibonacci digit sum 21 in base 10.
10956 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 10956 results in a sphenic number.
10956 = 13 + 163 + 193 is the sum of 3 positive cubes in 1 way.
10956 = 27402 - 27382 = 9162 - 9102 = 2602 - 2382 = 1162 - 502 is the difference of 2 nonnegative squares in 4 ways.
10956 is the sum of 2 positive triangular numbers.
10956 is the difference of 2 positive pentagonal numbers in 1 way.
10956 = 342 + 702 + 702 is the sum of 3 positive squares.
109562 is the sum of 3 positive squares.
10956 is a proper divisor of 3312 - 1.
10956 is palindromic in (at least) base -47.
10956 in base 39 = 77a and consists of only the digits '7' and 'a'.
10956 in base 46 = 588 and consists of only the digits '5' and '8'.

The number 10956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106455: Sequence A106456 interpreted as binary numbers and converted to decimal.
A111533: Row 6 of table A111528.
A114939: Number of essentially different seating arrangements for n couples around a circular table with 2n seats avoiding spouses being neighbors and avoiding clusters of 3 persons with equal gender.
A123862: Expansion of f(q)*f(q^7)/(f(-q)*f(-q^7)) in powers of q where f() is a Ramanujan theta function.
A133242: Indices n such that A134204(n) < n.
A210860: Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
A213818: Antidiagonal sums of the convolution array A213773.
A232137: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A281864: Number of sets of exactly four positive integers <= n having a square element sum.
A289227: Number of ways to select 6 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

Monday, July 24, 2017

Number of the day: 94536

Properties of the number 94536:

94536 = 23 × 32 × 13 × 101 is the 85419th composite number and is not squarefree.
94536 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 28800 totatives.
94536 has a triangular digit product 3240 in base 10.
94536 is the difference of 2 nonnegative squares in 12 ways.
94536 is the sum of 2 positive triangular numbers.
94536 is the difference of 2 positive pentagonal numbers in 3 ways.
94536 = 902 + 2942 = 302 + 3062 is the sum of 2 positive squares in 2 ways.
94536 = 162 + 742 + 2982 is the sum of 3 positive squares.
945362 = 529202 + 783362 = 363602 + 872642 = 183602 + 927362 = 187202 + 926642 is the sum of 2 positive squares in 4 ways.
945362 is the sum of 3 positive squares.
94536 is a proper divisor of 10094 - 1.
94536 = '9453' + '6' is the concatenation of 2 triangular numbers.
94536 is palindromic in (at least) the following bases: -57, and -95.
94536 in base 56 = U88 and consists of only the digits '8' and 'U'.

The number 94536 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A012698: E.g.f.: sin(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A012704: arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A187277: Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS.
A192770: Numbers n such that n^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two.
A195674: Numbers that are formed using their own digits and addition and seventh power operators.
A199924: Numbers n such that the sum of the largest and the smallest prime divisor of n^2 + 1 equals the sum of the other distinct prime divisors.
A215950: Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8.

Sunday, July 23, 2017

Number of the day: 790843

Properties of the number 790843:

790843 is a cyclic number.
790843 is the 63272th prime.
790843 has 29 antidivisors and 790842 totatives.
790843 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 790843 results in an emirp.
790843 = 3954222 - 3954212 is the difference of 2 nonnegative squares in 1 way.
790843 is the sum of 2 positive triangular numbers.
790843 is the difference of 2 positive pentagonal numbers in 1 way.
790843 = 1232 + 1552 + 8672 is the sum of 3 positive squares.
7908432 is the sum of 3 positive squares.
790843 is a proper divisor of 191339 - 1.
790843 is an emirp in (at least) the following bases: 5, 8, 10, 11, 19, 21, 23, 26, 28, 29, 30, 31, 41, 44, 54, 61, 64, 67, 76, 85, 86, 89, 94, 97, 99, and 100.

Saturday, July 22, 2017

Number of the day: 7222017

Happy Casual π Day!

Properties of the number 7222017:

7222017 is a cyclic number.
7222017 = 3 × 11 × 218849 is a sphenic number and squarefree.
7222017 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4376960 totatives.
7222017 has a semiprime digit sum 21 in base 10.
7222017 has a Fibonacci digit sum 21 in base 10.
7222017 has a triangular digit sum 21 in base 10.
7222017 = 36110092 - 36110082 = 12036712 - 12036682 = 3282792 - 3282682 = 1094412 - 1094082 is the difference of 2 nonnegative squares in 4 ways.
7222017 is the difference of 2 positive pentagonal numbers in 2 ways.
7222017 = 532 + 2182 + 26782 is the sum of 3 positive squares.
72220172 = 30162002 + 65620172 is the sum of 2 positive squares in 1 way.
72220172 is the sum of 3 positive squares.
7222017 is a proper divisor of 3976839 - 1.

Friday, July 21, 2017

Number of the day: 1844

Properties of the number 1844:

1844 = 22 × 461 is the 1561th composite number and is not squarefree.
1844 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 920 totatives.
1844 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 1844 results in a prime.
1844 = 13 + 83 + 113 is the sum of 3 positive cubes in 1 way.
1844 = 4622 - 4602 is the difference of 2 nonnegative squares in 1 way.
1844 is the difference of 2 positive pentagonal numbers in 1 way.
1844 = 202 + 382 is the sum of 2 positive squares in 1 way.
1844 = 102 + 122 + 402 is the sum of 3 positive squares.
18442 = 10442 + 15202 is the sum of 2 positive squares in 1 way.
18442 is the sum of 3 positive squares.
1844 is a proper divisor of 5094 - 1.
1844 is palindromic in (at least) the following bases: 20, -13, -14, -23, and -97.
1844 in base 13 = abb and consists of only the digits 'a' and 'b'.
1844 in base 17 = 668 and consists of only the digits '6' and '8'.
1844 in base 20 = 4c4 and consists of only the digits '4' and 'c'.
1844 in base 42 = 11c and consists of only the digits '1' and 'c'.

The number 1844 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014561: Numbers n giving rise to prime quadruples (30n+11, 30n+13, 30n+17, 30n+19).
A024026: a(n) = 3^n - n^3.
A067979: Triangle read by rows of incomplete convolutions of Lucas numbers L(n+1) = A000204(n+1), n>=0.
A067990: Triangle A067979 with rows read backwards.
A118551: a(0)=1. a(n) = a(n-1)*2, if n is in the sequence. a(n) = a(n-1) + 1 if n is missing from the sequence.
A134619: Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a prime.
A138920: Indices k such that A020509(k)=Phi[k](-10) is prime, where Phi is a cyclotomic polynomial.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A181470: Numbers n such that 97 is the largest prime factor of n^2-1.
A265067: Coordination sequence for (2,5,8) tiling of hyperbolic plane.

Thursday, July 20, 2017

Number of the day: 6052

Properties of the number 6052:

6052 = 22 × 17 × 89 is the 5262th composite number and is not squarefree.
6052 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2816 totatives.
6052 has an emirp digit sum 13 in base 10.
6052 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 6052 results in a sphenic number.
6052 = (53 × 54)/2 + … + (56 × 57)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6052 = 15142 - 15122 = 1062 - 722 is the difference of 2 nonnegative squares in 2 ways.
6052 is the difference of 2 positive pentagonal numbers in 1 way.
6052 = 542 + 562 = 242 + 742 is the sum of 2 positive squares in 2 ways.
6052 = 342 + 362 + 602 is the sum of 3 positive squares.
60522 = 28482 + 53402 = 2202 + 60482 = 35522 + 49002 = 26522 + 54402 is the sum of 2 positive squares in 4 ways.
60522 is the sum of 3 positive squares.
6052 is a proper divisor of 11234 - 1.
6052 is palindromic in (at least) the following bases: 36, 50, 55, 88, -31, -42, and -55.
6052 in base 6 = 44004 and consists of only the digits '0' and '4'.
6052 in base 27 = 884 and consists of only the digits '4' and '8'.
6052 in base 35 = 4ww and consists of only the digits '4' and 'w'.
6052 in base 36 = 4o4 and consists of only the digits '4' and 'o'.
6052 in base 49 = 2PP and consists of only the digits '2' and 'P'.
6052 in base 50 = 2L2 and consists of only the digits '2' and 'L'.
6052 in base 54 = 244 and consists of only the digits '2' and '4'.
6052 in base 55 = 202 and consists of only the digits '0' and '2'.

The number 6052 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006128: Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n.
A018813: Number of lines through exactly 6 points of an n X n grid of points.
A028305: Triangle of numbers of permutations eliminating just k cards out of n in game of Mousetrap.
A101709: Number of partitions of n having nonnegative even rank (the rank of a partition is the largest part minus the number of parts).
A108099: a(n) = 8n^2 + 8n + 4.
A122919: Inverse of Riordan array (1/(1+x+x^2),x/(1+x)^2).
A237832: Number of partitions of n such that (greatest part) - (least part) = number of parts.
A244385: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + ... + n^37 is prime.
A272423: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 473", based on the 5-celled von Neumann neighborhood.
A277449: Numbers n such that there is exactly one nontrivial square n-gonal number.

Wednesday, July 19, 2017

Number of the day: 4274

Properties of the number 4274:

4274 = 2 × 2137 is semiprime and squarefree.
4274 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 2136 totatives.
4274 has an emirp digit sum 17 in base 10.
4274 has sum of divisors equal to 6414 which is a sphenic number.
4274 = 72 + 652 is the sum of 2 positive squares in 1 way.
4274 = 152 + 322 + 552 is the sum of 3 positive squares.
42742 = 9102 + 41762 is the sum of 2 positive squares in 1 way.
42742 is the sum of 3 positive squares.
4274 is a proper divisor of 26389 - 1.
4274 = '4' + '274' is the concatenation of 2 semiprime numbers.
4274 is an emirpimes in (at least) the following bases: 3, 4, 13, 14, 16, 17, 25, 27, 28, 29, 31, 34, 35, 36, 38, 39, 44, 45, 52, 56, 57, 61, 64, 68, 69, 70, 73, 75, 80, 87, 89, 91, 94, 97, and 99.
4274 is palindromic in (at least) the following bases: -35, and -48.

The number 4274 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007498: Unique period lengths of primes mentioned in A007615.
A051627: Periods associated with A040017.
A125754: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has an integer solution, n is a term in the sequence.
A125756: Numbers n whose reverse binary representation has the following property: let a 0 mean "halving" and a 1 mean "k -> 3k+1". The number describes an operation k -> f_n(k). If the equation f_n(k) = k has a positive integer solution, n is a term in the sequence.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A201077: G.f.: 1 / Product_{i>=1} (1-q^(2*i-1))^2*(1-q^(12*i-8))*(1-q^(12*i-6))*(1-q^(12*i-4))*(1-q^(12*i)).
A217891: T(n,k)=Number of n element 1..n arrays with each element the minimum of k adjacent elements of a permutation of 1..n+k-1 of n+k-1 elements
A267167: Growth series for affine Coxeter group B_4.
A275188: Positions of 8 in A274640.
A278784: Numbers n such that A000041(n) is of the form 2^7 * k for odd k.

Tuesday, July 18, 2017

Number of the day: 3045

Properties of the number 3045:

3045 = 3 × 5 × 7 × 29 is the 2608th composite number and is squarefree.
3045 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1344 totatives.
3045 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3045 results in a semiprime.
3045 = 15232 - 15222 = 5092 - 5062 = 3072 - 3022 = 2212 - 2142 = 1092 - 942 = 832 - 622 = 672 - 382 = 612 - 262 is the difference of 2 nonnegative squares in 8 ways.
3045 is the sum of 2 positive triangular numbers.
3045 is the difference of 2 positive pentagonal numbers in 3 ways.
3045 = 202 + 232 + 462 is the sum of 3 positive squares.
30452 = 21002 + 22052 = 3572 + 30242 = 5042 + 30032 = 18272 + 24362 is the sum of 2 positive squares in 4 ways.
30452 is the sum of 3 positive squares.
3045 is a proper divisor of 3492 - 1.
3045 is palindromic in (at least) base 86.
3045 in base 12 = 1919 and consists of only the digits '1' and '9'.
3045 in base 14 = 1177 and consists of only the digits '1' and '7'.
3045 in base 19 = 885 and consists of only the digits '5' and '8'.
3045 in base 22 = 669 and consists of only the digits '6' and '9'.
3045 in base 27 = 44l and consists of only the digits '4' and 'l'.

The number 3045 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000266: E.g.f. exp(-x^2/2) / (1-x).
A005476: a(n) = n*(5*n - 1)/2.
A007059: Number of balanced ordered trees with n nodes.
A022289: a(n) = n*(31*n + 1)/2.
A024966: 7 times triangular numbers: 7n(n+1)/2.
A034828: a(n) = [n^2/4]*n/2.
A055561: Numbers n such that there are precisely 3 groups of order n.
A079500: Number of compositions of the integer n in which the first part is >= the other parts.
A094416: Array read by antidiagonals: generalized ordered Bell numbers Bo(r,n).
A128396: Numbers n such that n^2 divides 16^n-1.

Monday, July 17, 2017

Number of the day: 7172017

Happy Yellow Pig Day!

Properties of the number 7172017:

7172017 is a cyclic number.
7172017 = 1877 × 3821 is semiprime and squarefree.
7172017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7166320 totatives.
7172017 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 7172017 results in a sphenic number.
7172017 = 35860092 - 35860082 = 28492 - 9722 is the difference of 2 nonnegative squares in 2 ways.
7172017 is the sum of 2 positive triangular numbers.
7172017 is the difference of 2 positive pentagonal numbers in 1 way.
7172017 = 12642 + 23612 = 4442 + 26412 is the sum of 2 positive squares in 2 ways.
7172017 = 862 + 1892 + 26702 is the sum of 3 positive squares.
71720172 = 43865082 + 56741852 = 39766252 + 59686082 = 23452082 + 67777452 = 22899402 + 67966172 is the sum of 2 positive squares in 4 ways.
71720172 is the sum of 3 positive squares.
7172017 is a proper divisor of 137764 - 1.
7172017 is an emirpimes in (at least) the following bases: 2, 8, 13, 19, 21, 22, 25, 26, 27, 31, 34, 35, 37, 38, 39, 44, 45, 51, 53, 59, 61, 67, 73, 75, 77, 80, 82, 83, 85, 87, 89, 91, 93, and 97.

Sunday, July 16, 2017

Number of the day: 81813

Properties of the number 81813:

81813 = 3 × 27271 is semiprime and squarefree.
81813 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 54540 totatives.
81813 has a semiprime digit sum 21 in base 10.
81813 has a Fibonacci digit sum 21 in base 10.
81813 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 81813 results in a sphenic number.
81813 = 409072 - 409062 = 136372 - 136342 is the difference of 2 nonnegative squares in 2 ways.
81813 is the sum of 2 positive triangular numbers.
81813 is the difference of 2 positive pentagonal numbers in 1 way.
81813 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
81813 = 12 + 42 + 2862 is the sum of 3 positive squares.
818132 is the sum of 3 positive squares.
81813 is a proper divisor of 190154 - 1.
81813 is an emirpimes in (at least) the following bases: 3, 6, 7, 9, 15, 19, 33, 35, 48, 51, 55, 61, 67, 71, 78, 81, 85, and 99.
81813 is palindromic in (at least) base -55.
81813 in base 54 = S33 and consists of only the digits '3' and 'S'.

The number 81813 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A053948: Numbers n such that n^2 contains only digits {3,6,9}.
A137041: Numbers n such that n and the square of n use only the digits 1, 3, 6, 8 and 9.

Saturday, July 15, 2017

Number of the day: 3509167

Properties of the number 3509167:

3509167 is a cyclic number.
3509167 = 19 × 184693 is semiprime and squarefree.
3509167 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 3324456 totatives.
3509167 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 3509167 results in a sphenic number.
3509167 = 17545842 - 17545832 = 923562 - 923372 is the difference of 2 nonnegative squares in 2 ways.
3509167 is the sum of 2 positive triangular numbers.
3509167 is the difference of 2 positive pentagonal numbers in 2 ways.
3509167 is not the sum of 3 positive squares.
35091672 = 21343082 + 27854952 is the sum of 2 positive squares in 1 way.
35091672 is the sum of 3 positive squares.
3509167 is a proper divisor of 3730782 - 1.
3509167 is an emirpimes in (at least) the following bases: 4, 6, 11, 13, 24, 25, 26, 31, 38, 42, 43, 44, 45, 47, 53, 55, 58, 64, 71, 76, 81, 83, 86, 87, 93, 95, 99, and 100.

The number 3509167 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A159339: Transform of A056594 by the T_{1,0} transformation (see link)

Friday, July 14, 2017

Number of the day: 96063

Properties of the number 96063:

96063 is a cyclic number.
96063 = 3 × 11 × 41 × 71 is the 86804th composite number and is squarefree.
96063 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 56000 totatives.
Reversing the decimal digits of 96063 results in a sphenic number.
96063 = 480322 - 480312 = 160122 - 160092 = 43722 - 43612 = 14722 - 14392 = 11922 - 11512 = 7122 - 6412 = 4522 - 3292 = 3322 - 1192 is the difference of 2 nonnegative squares in 8 ways.
96063 is the sum of 2 positive triangular numbers.
96063 is the difference of 2 positive pentagonal numbers in 4 ways.
96063 is not the sum of 3 positive squares.
960632 = 210872 + 937202 is the sum of 2 positive squares in 1 way.
960632 is the sum of 3 positive squares.
96063 is a proper divisor of 28310 - 1.
96063 is palindromic in (at least) the following bases: 85, and -62.
96063 in base 61 = Pnn and consists of only the digits 'P' and 'n'.

The number 96063 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115132: Partial sums of A064059.
A123789: Number of ways, counted up to symmetry, to build a contiguous building with n LEGO blocks of size 1x5 which is flat, i.e. with all blocks in parallel position and symmetric after a rotation by 180 degrees.

Wednesday, July 12, 2017

Number of the day: 378349

Properties of the number 378349:

378349 is a cyclic number.
378349 = 67 × 5647 is semiprime and squarefree.
378349 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 372636 totatives.
378349 has a semiprime digit sum 34 in base 10.
378349 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 378349 results in an emirpimes.
378349 = (71 × 72)/2 + … + (137 × 138)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
378349 = 1891752 - 1891742 = 28572 - 27902 is the difference of 2 nonnegative squares in 2 ways.
378349 is the sum of 2 positive triangular numbers.
378349 is the difference of 2 positive pentagonal numbers in 2 ways.
378349 = 722 + 772 + 6062 is the sum of 3 positive squares.
3783492 is the sum of 3 positive squares.
378349 is a proper divisor of 85333 - 1.
378349 = '37834' + '9' is the concatenation of 2 semiprime numbers.
378349 is an emirpimes in (at least) the following bases: 2, 10, 11, 12, 16, 18, 26, 27, 28, 32, 34, 42, 43, 45, 46, 47, 51, 55, 58, 60, 62, 63, 64, 65, 67, 69, 70, 71, 73, 75, 83, 91, 93, 94, 96, 97, and 100.
378349 is palindromic in (at least) base -92.