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).