Tuesday, February 28, 2017

Number of the day: 39093501740

Pierre Joseph Louis Fatou was born on this day 139 years ago.

Properties of the number 39093501740:

39093501740 = 22 × 5 × 557 × 3509291 is composite and not squarefree.
39093501740 has 4 distinct prime factors, 24 divisors, 25 antidivisors and 15609321920 totatives.
39093501740 has a prime digit sum 41 in base 10.
39093501740 = 97733754362 - 97733754342 = 19546750922 - 19546750822 = 175470122 - 175458982 = 35120762 - 35065062 is the difference of 2 nonnegative squares in 4 ways.
39093501740 is the difference of 2 positive pentagonal numbers in 4 ways.
39093501740 = 102 + 10462 + 1977182 is the sum of 3 positive squares.
390935017402 = 234561010442 + 312748013922 = 131387855042 + 368194811722 = 229226888122 + 316678419842 = 115806603002 + 373388562402 is the sum of 2 positive squares in 4 ways.
390935017402 is the sum of 3 positive squares.
39093501740 is a divisor of 1553242020 - 1.

Monday, February 27, 2017

Number of the day: 717335

Luitzen Egbertus Jan Brouwer was born on this day 136 years ago.

Properties of the number 717335:

717335 = 5 × 143467 is semiprime and squarefree.
717335 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 573864 totatives.
717335 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 717335 results in an emirpimes.
717335 = 3586682 - 3586672 = 717362 - 717312 is the difference of 2 nonnegative squares in 2 ways.
717335 is the difference of 2 positive pentagonal numbers in 2 ways.
717335 is not the sum of 3 positive squares.
7173352 = 4304012 + 5738682 is the sum of 2 positive squares in 1 way.
7173352 is the sum of 3 positive squares.
717335 is a divisor of 4123911 - 1.
717335 = '717' + '335' is the concatenation of 2 semiprime numbers.
717335 is an emirpimes in (at least) the following bases: 5, 10, 15, 17, 19, 22, 23, 28, 31, 37, 38, 40, 41, 45, 46, 47, 50, 61, 62, 63, 65, 69, 82, 84, 87, 93, 94, 95, and 97.

Sunday, February 26, 2017

Number of the day: 620469

Properties of the number 620469:

620469 = 32 × 71 × 971 is the 569819th composite number and is not squarefree.
620469 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 407400 totatives.
620469 = 3102352 - 3102342 = 1034132 - 1034102 = 344752 - 344662 = 44052 - 43342 = 15632 - 13502 = 8052 - 1662 is the difference of 2 nonnegative squares in 6 ways.
620469 is the sum of 2 positive triangular numbers.
620469 is the difference of 2 positive pentagonal numbers in 1 way.
620469 = 222 + 732 + 7842 is the sum of 3 positive squares.
6204692 is the sum of 3 positive squares.
620469 is a divisor of 160170 - 1.
620469 = '6' + '20469' is the concatenation of 2 semiprime numbers.
620469 is palindromic in (at least) base -19.
620469 in base 21 = 33kk3 and consists of only the digits '3' and 'k'.

Saturday, February 25, 2017

Number of the day: 839584494279

Properties of the number 839584494279:

839584494279 = 32 × 43789 × 2130379 is composite and not squarefree.
839584494279 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 559709951184 totatives.
839584494279 has an oblong digit sum 72 in base 10.
839584494279 = 4197922471402 - 4197922471392 = 1399307490482 - 1399307490452 = 466435830202 - 466435830112 = 96086002 - 95648112 = 32612522 - 31298852 = 12622402 - 8681392 is the difference of 2 nonnegative squares in 6 ways.
839584494279 is the difference of 2 positive pentagonal numbers in 2 ways.
839584494279 is not the sum of 3 positive squares.
8395844942792 = 3301661374202 + 7719407002712 is the sum of 2 positive squares in 1 way.
8395844942792 is the sum of 3 positive squares.
839584494279 is a divisor of 35387345498 - 1.
839584494279 = '83958449' + '4279' is the concatenation of 2 semiprime numbers.

Friday, February 24, 2017

Number of the day: 3504

Properties of the number 3504:

3504 = 24 × 3 × 73 is the 3014th composite number and is not squarefree.
3504 has 3 distinct prime factors, 20 divisors, 15 antidivisors and 1152 totatives.
3504 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 3504 results in a sphenic number.
3504 = 8772 - 8752 = 4402 - 4362 = 2952 - 2892 = 2232 - 2152 = 1522 - 1402 = 852 - 612 is the difference of 2 nonnegative squares in 6 ways.
3504 is the difference of 2 positive pentagonal numbers in 1 way.
3504 = 202 + 202 + 522 is the sum of 3 positive squares.
35042 = 23042 + 26402 is the sum of 2 positive squares in 1 way.
35042 is the sum of 3 positive squares.
3504 is a divisor of 4392 - 1.
3504 is palindromic in (at least) the following bases: 28, and 72.
3504 in base 8 = 6660 and consists of only the digits '0' and '6'.
3504 in base 17 = c22 and consists of only the digits '2' and 'c'.
3504 in base 27 = 4ll and consists of only the digits '4' and 'l'.
3504 in base 28 = 4d4 and consists of only the digits '4' and 'd'.
3504 in base 29 = 44o and consists of only the digits '4' and 'o'.

The number 3504 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001106: 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.
A033580: Four times second pentagonal numbers: a(n) = 2*n*(3*n+1).
A050208: Starting positions of strings of 2 1's in the decimal expansion of Pi.
A062717: Numbers m such that 6*m+1 is a perfect square.
A105078: Positive integers n such that n^10 + 1 is semiprime.
A183517: T(n,k)=Number of nXk binary arrays with each element equal to either the sum mod 2 of its horizontal and vertical neighbors or the sum mod 2 of its diagonal and antidiagonal neighbors
A199943: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zeroth through n-1st differences all nonzero
A201155: T(n,k)=Number of nXk 0..2 arrays with every diagonal, row and column running average nondecreasing rightwards and downwards and diagonally
A207100: T(n,k)=Number of 0..k arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo (k+1)
A235954: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the upper median value of each 2X2 subblock

Thursday, February 23, 2017

Number of the day: 7844811

Properties of the number 7844811:

7844811 = 3 × 132 × 15473 is the 7314806th composite number and is not squarefree.
7844811 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 4827264 totatives.
7844811 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 7844811 results in a semiprime.
7844811 = 39224062 - 39224052 = 13074702 - 13074672 = 3017302 - 3017172 = 1005942 - 1005552 = 232942 - 231252 = 79902 - 74832 is the difference of 2 nonnegative squares in 6 ways.
7844811 is the difference of 2 positive pentagonal numbers in 3 ways.
7844811 = 1692 + 2452 + 27852 is the sum of 3 positive squares.
78448112 = 51029552 + 59582642 = 24187802 + 74626112 = 35372612 + 70020602 = 6375152 + 78188642 = 5720642 + 78239252 = 30172352 + 72413642 = 55238612 + 55702802 is the sum of 2 positive squares in 7 ways.
78448112 is the sum of 3 positive squares.
7844811 is a divisor of 5777736 - 1.

Wednesday, February 22, 2017

Number of the day: 31743487794220

Frank Plumpton Ramsey was born on this day 114 years ago.

Properties of the number 31743487794220:

31743487794220 = 22 × 5 × 277 × 5729871443 is composite and not squarefree.
31743487794220 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 12651556143936 totatives.
31743487794220 has a prime digit sum 61 in base 10.
31743487794220 = 79358719485562 - 79358719485542 = 15871743897162 - 15871743897062 = 286493574922 - 286493569382 = 57298728282 - 57298700582 is the difference of 2 nonnegative squares in 4 ways.
31743487794220 is the sum of 2 positive triangular numbers.
31743487794220 is the difference of 2 positive pentagonal numbers in 4 ways.
31743487794220 = 41542 + 191102 + 56341022 is the sum of 3 positive squares.
317434877942202 = 190460926765322 + 253947902353762 = 67841677885122 + 310100642495162 = 151956190668362 + 278700946987522 = 131787043189002 + 288785520727202 is the sum of 2 positive squares in 4 ways.
317434877942202 is the sum of 3 positive squares.
31743487794220 is a divisor of 2232961506588 - 1.

Tuesday, February 21, 2017

Number of the day: 354158497701

Properties of the number 354158497701:

354158497701 = 32 × 97 × 405679837 is composite and not squarefree.
354158497701 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 233671585536 totatives.
354158497701 = 1770792488512 - 1770792488502 = 590264162852 - 590264162822 = 196754720992 - 196754720902 = 18255593152 - 18255592182 = 6085199012 - 6085196102 = 2028403552 - 2028394822 is the difference of 2 nonnegative squares in 6 ways.
354158497701 is the difference of 2 positive pentagonal numbers in 2 ways.
354158497701 = 4011902 + 4395512 = 574262 + 5923352 is the sum of 2 positive squares in 2 ways.
354158497701 = 792 + 4462 + 5951122 is the sum of 3 positive squares.
3541584977012 = 2373227046452 + 2628805343762 = 680308594202 + 3475630067492 = 322516655012 + 3526869313802 = 2123972229242 + 2834001785252 is the sum of 2 positive squares in 4 ways.
3541584977012 is the sum of 3 positive squares.
354158497701 is a divisor of 1093445264 - 1.
354158497701 = '35' + '4158497701' is the concatenation of 2 semiprime numbers.

Monday, February 20, 2017

Number of the day: 361394

Properties of the number 361394:

361394 = 2 × 11 × 16427 is a sphenic number and squarefree.
361394 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 164260 totatives.
361394 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 361394 results in a sphenic number.
361394 is the difference of 2 positive pentagonal numbers in 2 ways.
361394 = 72 + 122 + 6012 is the sum of 3 positive squares.
3613942 is the sum of 3 positive squares.
361394 is a divisor of 1277191 - 1.
361394 = '361' + '394' is the concatenation of 2 semiprime numbers.
361394 is palindromic in (at least) base 90.

Sunday, February 19, 2017

Number of the day: 7127

Properties of the number 7127:

7127 and 7129 form a twin prime pair.
7127 has 5 antidivisors and 7126 totatives.
7127 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 7127 results in a semiprime.
7127 = 35642 - 35632 is the difference of 2 nonnegative squares in 1 way.
7127 is the difference of 2 positive pentagonal numbers in 1 way.
7127 is not the sum of 3 positive squares.
71272 is the sum of 3 positive squares.
7127 is a divisor of 3509 - 1.
7127 = '7' + '127' is the concatenation of 2 prime numbers.
7127 is an emirp in (at least) the following bases: 2, 6, 7, 11, 13, 18, 19, 20, 21, 25, 37, 39, 41, 43, 49, 53, 55, 60, 65, 76, 84, 85, 90, and 93.
7127 is palindromic in (at least) the following bases: 57, -52, and -75.
7127 in base 6 = 52555 and consists of only the digits '2' and '5'.
7127 in base 13 = 3323 and consists of only the digits '2' and '3'.
7127 in base 56 = 2FF and consists of only the digits '2' and 'F'.
7127 in base 57 = 2B2 and consists of only the digits '2' and 'B'.
7127 in base 59 = 22l and consists of only the digits '2' and 'l'.

The number 7127 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000945: Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).
A045713: Primes with first digit 7.
A050268: Primes of the form 36*n^2 - 810*n + 2753, listed in order of increasing parameter n >= 0.
A090287: Smallest prime obtained by sandwiching n between a number with identical digits, or 0 if no such prime exists. Primes of the form k n k where all the digits of k are identical.
A129658: Numerators of the convergents of the continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
A134971: Canyon primes.
A136074: Father primes of order 5.
A174913: Lesser of twin primes p1 such that 2*p1+p2 is a prime number.
A204867: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly two different ways, and new values 0..1 introduced in row major order
A263358: Expansion of Product_{k>=1} 1/(1-x^(k+2))^k.

Friday, February 17, 2017

Number of the day: 803782

Properties of the number 803782:

803782 = 2 × 7 × 57413 is a sphenic number and squarefree.
803782 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 344472 totatives.
803782 has a triangular digit sum 28 in base 10.
803782 is the difference of 2 positive pentagonal numbers in 4 ways.
803782 = 102 + 992 + 8912 is the sum of 3 positive squares.
8037822 = 2391902 + 7673682 is the sum of 2 positive squares in 1 way.
8037822 is the sum of 3 positive squares.
803782 is a divisor of 18162 - 1.
803782 is palindromic in (at least) base -98.

Thursday, February 16, 2017

Number of the day: 118176156951

Properties of the number 118176156951:

118176156951 = 3 × 83617 × 471101 is a sphenic number and squarefree.
118176156951 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 78782995200 totatives.
118176156951 has an emirpimes digit sum 51 in base 10.
118176156951 = 590880784762 - 590880784752 = 196960261602 - 196960261572 = 7484602 - 6648432 = 3609762 - 1101252 is the difference of 2 nonnegative squares in 4 ways.
118176156951 is the sum of 2 positive triangular numbers.
118176156951 is the difference of 2 positive pentagonal numbers in 1 way.
118176156951 is not the sum of 3 positive squares.
1181761569512 = 668486464652 + 974518472762 = 599353536242 + 1018496806952 = 111208598762 + 1176517341452 = 500849106602 + 1070378708492 is the sum of 2 positive squares in 4 ways.
1181761569512 is the sum of 3 positive squares.
118176156951 is a divisor of 11232164368 - 1.
118176156951 = '118' + '176156951' is the concatenation of 2 semiprime numbers.

Wednesday, February 15, 2017

Number of the day: 40573506153901

Galileo Galilei was born on this day 453 years ago.

Alfred North Whitehead was born on this day 156 years ago.

Properties of the number 40573506153901:

40573506153901 = 7 × 151 × 421 × 91177033 is composite and squarefree.
40573506153901 has 4 distinct prime factors, 16 divisors, 47 antidivisors and 34464918096000 totatives.
40573506153901 has an emirpimes digit sum 49 in base 10.
40573506153901 = 202867530769512 - 202867530769502 = 28981075824252 - 28981075824182 = 1343493582012 - 1343493580502 = 481870621512 - 481870617302 = 191927659752 - 191927649182 = 68838674652 - 68838645182 = 3191514012 - 3190878302 = 458110152 - 453660182 is the difference of 2 nonnegative squares in 8 ways.
40573506153901 is the sum of 2 positive triangular numbers.
40573506153901 is the difference of 2 positive pentagonal numbers in 8 ways.
40573506153901 = 79402 + 354512 + 63696302 is the sum of 3 positive squares.
405735061539012 = 216507024792242 + 343140857925252 = 192355975137552 + 357239582060762 = 239629537512052 + 327412010949242 = 27948495925492 + 404771320300202 is the sum of 2 positive squares in 4 ways.
405735061539012 is the sum of 3 positive squares.
40573506153901 is a divisor of 166356985645 - 1.

Tuesday, February 14, 2017

Number of the day: 369685

Properties of the number 369685:

369685 = 5 × 107 × 691 is a sphenic number and squarefree.
369685 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 292560 totatives.
369685 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 369685 results in a sphenic number.
369685 = 1848432 - 1848422 = 369712 - 369662 = 17812 - 16742 = 6132 - 782 is the difference of 2 nonnegative squares in 4 ways.
369685 is the sum of 2 positive triangular numbers.
369685 is the difference of 2 positive pentagonal numbers in 3 ways.
369685 = 1612 + 1802 + 5582 is the sum of 3 positive squares.
3696852 = 2218112 + 2957482 is the sum of 2 positive squares in 1 way.
3696852 is the sum of 3 positive squares.
369685 is a divisor of 1381106 - 1.
369685 is palindromic in (at least) base 95.
369685 in base 58 = 1ppp and consists of only the digits '1' and 'p'.

Monday, February 13, 2017

Number of the day: 8512

Peter Gustav Lejeune Dirichlet was born on this day 212 years ago.

Properties of the number 8512:

8512 = 26 × 7 × 19 is the 7451th composite number and is not squarefree.
8512 has 3 distinct prime factors, 28 divisors, 15 antidivisors and 3456 totatives.
Reversing the decimal digits of 8512 results in a sphenic number.
8512 = 203 + 83 is the sum of 2 positive cubes in 1 way.
8512 is the difference of 2 nonnegative squares in 10 ways.
8512 is the difference of 2 positive pentagonal numbers in 3 ways.
8512 = 322 + 482 + 722 is the sum of 3 positive squares.
85122 is the sum of 3 positive squares.
8512 is a divisor of 12172 - 1.
8512 is palindromic in (at least) the following bases: -35, and -74.
8512 in base 23 = g22 and consists of only the digits '2' and 'g'.
8512 in base 34 = 7cc and consists of only the digits '7' and 'c'.

The number 8512 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007764: Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid.
A037032: Total number of prime parts in all partitions of n.
A064298: Square array read by antidiagonals of self-avoiding rook paths joining opposite corners of n X k board.
A115176: Positive numbers that are not the sum of two squares and a positive Fibonacci number.
A139267: Twice octagonal numbers: 2*n*(3*n-2).
A179672: Products of the 6st power of a prime and 2 distinct primes (p^6*q*r).
A188211: T(n,k)=Number of nondecreasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero
A243953: E.g.f.: exp( Sum_{n>=1} A000108(n-1)*x^n/n ), where A000108(n) = binomial(2*n,n)/(n+1) forms the Catalan numbers.
A251088: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements
A257417: Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.

Sunday, February 12, 2017

Number of the day: 818983

Properties of the number 818983:

818983 = 11 × 74453 is semiprime and squarefree.
818983 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 744520 totatives.
818983 has an emirp digit sum 37 in base 10.
818983 = 4094922 - 4094912 = 372322 - 372212 is the difference of 2 nonnegative squares in 2 ways.
818983 is the sum of 2 positive triangular numbers.
818983 is the difference of 2 positive pentagonal numbers in 2 ways.
818983 is not the sum of 3 positive squares.
8189832 = 3753752 + 7278922 is the sum of 2 positive squares in 1 way.
8189832 is the sum of 3 positive squares.
818983 is a divisor of 6172659 - 1.
818983 is an emirpimes in (at least) the following bases: 4, 11, 14, 15, 20, 22, 27, 29, 30, 31, 33, 36, 37, 41, 48, 49, 53, 54, 59, 66, 69, 73, 76, 77, 78, 82, 83, 86, 88, 89, 93, and 95.

Saturday, February 11, 2017

Number of the day: 35915

Properties of the number 35915:

35915 = 5 × 11 × 653 is a sphenic number and squarefree.
35915 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 26080 totatives.
35915 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 35915 results in a semiprime.
35915 = 192 + … + 482 is the sum of at least 2 consecutive positive squares in 1 way.
35915 = 179582 - 179572 = 35942 - 35892 = 16382 - 16272 = 3542 - 2992 is the difference of 2 nonnegative squares in 4 ways.
35915 is the difference of 2 positive pentagonal numbers in 4 ways.
35915 = 52 + 132 + 1892 is the sum of 3 positive squares.
359152 = 215492 + 287322 = 50162 + 355632 = 147732 + 327362 = 173252 + 314602 is the sum of 2 positive squares in 4 ways.
359152 is the sum of 3 positive squares.
35915 is a divisor of 14920 - 1.
35915 is palindromic in (at least) the following bases: -50, and -90.
35915 in base 33 = wwb and consists of only the digits 'b' and 'w'.
35915 in base 39 = NNZ and consists of only the digits 'N' and 'Z'.

The number 35915 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A037279: If n is composite, replace n by the concatenation of its proper divisors, otherwise a(n) = n.
A037280: If n is composite replace n by the concatenation of its nontrivial divisors [ A037279 ] then divide out any factors of 2.
A037285: Replace n by concatenation of its nontrivial odd divisors.
A037288: Replace 2n+1 by concatenation of its nontrivial divisors.
A106708: Replace n by the concatenation of its proper divisors (a(n) = 0 unless n is composite).

Friday, February 10, 2017

Number of the day: 848379076327753

Properties of the number 848379076327753:

848379076327753 is prime.
848379076327753 has 45 antidivisors and 848379076327752 totatives.
848379076327753 has an emirp digit sum 79 in base 10.
848379076327753 has sum of divisors equal to 848379076327754 which is a sphenic number.
848379076327753 = 4241895381638772 - 4241895381638762 is the difference of 2 nonnegative squares in 1 way.
848379076327753 is the difference of 2 positive pentagonal numbers in 1 way.
848379076327753 = 50815572 + 286802522 is the sum of 2 positive squares in 1 way.
848379076327753 = 63212 + 72862 + 291269462 is the sum of 3 positive squares.
8483790763277532 = 2914806706247282 + 7967346332392552 is the sum of 2 positive squares in 1 way.
8483790763277532 is the sum of 3 positive squares.
848379076327753 is a divisor of 1451364424001859 - 1.
848379076327753 = '84837' + '9076327753' is the concatenation of 2 semiprime numbers.
848379076327753 is an emirp in (at least) the following bases: 14, 23, 30, 37, 45, 54, 69, 81, 89, and 93.

Thursday, February 9, 2017

Number of the day: 9641

Properties of the number 9641:

9641 = 31 × 311 is semiprime and squarefree.
9641 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 9300 totatives.
9641 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 9641 results in an emirpimes.
9641 = 48212 - 48202 = 1712 - 1402 is the difference of 2 nonnegative squares in 2 ways.
9641 is the sum of 2 positive triangular numbers.
9641 is the difference of 2 positive pentagonal numbers in 2 ways.
9641 = 12 + 62 + 982 is the sum of 3 positive squares.
96412 is the sum of 3 positive squares.
9641 is a divisor of 154910 - 1.
9641 is an emirpimes in (at least) the following bases: 2, 5, 6, 8, 10, 11, 13, 15, 16, 20, 21, 23, 25, 27, 33, 34, 36, 40, 45, 49, 50, 51, 53, 54, 56, 61, 64, 66, 70, 72, 73, 74, 75, 76, 78, 79, 81, 82, 84, 85, 86, 88, 91, 94, 98, and 99.
9641 is palindromic in (at least) the following bases: 32, 63, -5, -24, -25, -30, -41, -44, -61, and -81.
9641 in base 4 = 2112221 and consists of only the digits '1' and '2'.
9641 in base 24 = ghh and consists of only the digits 'g' and 'h'.
9641 in base 29 = bdd and consists of only the digits 'b' and 'd'.
9641 in base 32 = 9d9 and consists of only the digits '9' and 'd'.
9641 in base 40 = 611 and consists of only the digits '1' and '6'.
9641 in base 43 = 599 and consists of only the digits '5' and '9'.
9641 in base 62 = 2VV and consists of only the digits '2' and 'V'.

The number 9641 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007419: Largest number not the sum of distinct n-th-order polygonal numbers.
A020223: Pseudoprimes to base 95.
A048698: Nonprime numbers n such that sum of aliquot divisors of n is a cube.
A049048: Composite numbers n such that k! == 1 (mod n) for some k > 2.
A055437: a(n) = 10*n^2+n.
A128356: Least number k>1 (that is not the power of prime p) such that k divides (p+1)^k-1, where p = prime(n).
A128452: Least number k>n such that k^2 divides n^k - 1.
A134602: Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
A135789: Positive numbers of the form x^4 - 6 * x^2 * y^2 + y^4 (where x,y are integers).
A247137: Numbers for which the root mean square of nontrivial divisors is an integer and which are not a square of prime numbers.

Wednesday, February 8, 2017

Number of the day: 3316478658132

Daniel Bernoulli was born on this day 317 years ago.

Properties of the number 3316478658132:

3316478658132 = 22 × 3 × 79 × 2833 × 1234873 is composite and not squarefree.
3316478658132 has 5 distinct prime factors, 48 divisors, 51 antidivisors and 1091113141248 totatives.
3316478658132 has a semiprime digit sum 57 in base 10.
Reversing the decimal digits of 3316478658132 results in a sphenic number.
3316478658132 = 8291196645342 - 8291196645322 = 2763732215142 - 2763732215082 = 104951857062 - 104951855482 = 34983954462 - 34983949722 = 2926677342 - 2926620682 = 975634662 - 975464682 = 39284262 - 34808122 = 19062942 - 5634522 is the difference of 2 nonnegative squares in 8 ways.
3316478658132 is the difference of 2 positive pentagonal numbers in 4 ways.
3316478658132 = 30202 + 70542 + 18211042 is the sum of 3 positive squares.
33164786581322 = 20779207971002 + 25848164056322 = 10868215176002 + 31333448068682 = 3881256181322 + 32936892984002 = 17611426543682 + 28102325955002 is the sum of 2 positive squares in 4 ways.
33164786581322 is the sum of 3 positive squares.
3316478658132 is a divisor of 293411624 - 1.

Tuesday, February 7, 2017

Number of the day: 272017

Godfrey Harold Hardy was born on this day 140 years ago.

Happy e-Day!

Properties of the number 272017:

272017 = 17 × 16001 is semiprime and squarefree.
272017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 256000 totatives.
272017 has a prime digit sum 19 in base 10.
272017 = 1360092 - 1360082 = 80092 - 79922 is the difference of 2 nonnegative squares in 2 ways.
272017 is the difference of 2 positive pentagonal numbers in 2 ways.
272017 = 2242 + 4712 = 242 + 5212 is the sum of 2 positive squares in 2 ways.
272017 = 12 + 2042 + 4802 is the sum of 3 positive squares.
2720172 = 1716652 + 2110082 = 1280082 + 2400152 = 250082 + 2708652 = 1054002 + 2507672 is the sum of 2 positive squares in 4 ways.
2720172 is the sum of 3 positive squares.
272017 is a divisor of 8316 - 1.
272017 is an emirpimes in (at least) the following bases: 2, 6, 7, 9, 11, 12, 13, 15, 17, 19, 20, 22, 25, 26, 29, 31, 33, 35, 37, 39, 41, 43, 47, 48, 49, 51, 53, 55, 56, 59, 60, 62, 70, 71, 73, 74, 76, 78, 79, 81, 85, 87, 89, 91, 95, and 96.
272017 is palindromic in (at least) base -97.

Monday, February 6, 2017

Number of the day: 956

Properties of the number 956:

956 = 22 × 239 is the 793th composite number and is not squarefree.
956 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 476 totatives.
956 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 956 results in a prime.
956 = 2402 - 2382 is the difference of 2 nonnegative squares in 1 way.
956 is the sum of 2 positive triangular numbers.
956 is the difference of 2 positive pentagonal numbers in 1 way.
956 is not the sum of 3 positive squares.
9562 is the sum of 3 positive squares.
956 is a divisor of 4792 - 1.
956 = '95' + '6' is the concatenation of 2 semiprime numbers.
956 is palindromic in (at least) the following bases: 14, 18, and -17.
956 in base 14 = 4c4 and consists of only the digits '4' and 'c'.
956 in base 18 = 2h2 and consists of only the digits '2' and 'h'.
956 in base 30 = 11q and consists of only the digits '1' and 'q'.

The number 956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003480: a(n) = 4a(n-1) - 2a(n-2) (n >= 3).
A006313: Numbers n such that n^16 + 1 is prime.
A006314: Numbers n such that n^8 + 1 is prime.
A023359: Number of compositions (ordered partitions) of n into powers of 2.
A060978: |First digit - second digit + third digit - fourth digit ...| = 10.
A087097: Lunar primes (formerly called dismal primes) (cf. A087062).
A161424: Numbers n such that their largest divisor <= sqrt(n) equals 4.
A231145: Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.
A235229: Numbers whose sum of digits is 20.
A238557: Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

Sunday, February 5, 2017

Number of the day: 491587949916

Properties of the number 491587949916:

491587949916 = 22 × 34 × 7 × 216749537 is composite and not squarefree.
491587949916 has 4 distinct prime factors, 60 divisors, 25 antidivisors and 140453699328 totatives.
491587949916 has an oblong digit sum 72 in base 10.
491587949916 is the difference of 2 nonnegative squares in 10 ways.
491587949916 is the difference of 2 positive pentagonal numbers in 2 ways.
491587949916 is not the sum of 3 positive squares.
4915879499162 = 1390416111002 + 4715147324162 is the sum of 2 positive squares in 1 way.
4915879499162 is the sum of 3 positive squares.
491587949916 is a divisor of 156740640538 - 1.

Saturday, February 4, 2017

Number of the day: 92645

Properties of the number 92645:

92645 = 5 × 7 × 2647 is a sphenic number and squarefree.
92645 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 63504 totatives.
92645 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 92645 results in a prime.
92645 = (190 × 191)/2 + … + (194 × 195)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
92645 = 463232 - 463222 = 92672 - 92622 = 66212 - 66142 = 13412 - 13062 is the difference of 2 nonnegative squares in 4 ways.
92645 is the difference of 2 positive pentagonal numbers in 4 ways.
92645 = 22 + 152 + 3042 is the sum of 3 positive squares.
926452 = 555872 + 741162 is the sum of 2 positive squares in 1 way.
926452 is the sum of 3 positive squares.
92645 is a divisor of 24118 - 1.
92645 is palindromic in (at least) base -97.

The number 92645 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A205483: L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d.
A239429: Numbers n such that n^6+6 and n^6-6 are prime.

Friday, February 3, 2017

Number of the day: 425448

Gaston Julia was born on this day 124 years ago.

Properties of the number 425448:

425448 = 23 × 32 × 19 × 311 is the 389632th composite number and is not squarefree.
425448 has 4 distinct prime factors, 48 divisors, 13 antidivisors and 133920 totatives.
425448 is the difference of 2 nonnegative squares in 12 ways.
425448 is the sum of 2 positive triangular numbers.
425448 is the difference of 2 positive pentagonal numbers in 3 ways.
425448 = 1042 + 1942 + 6142 is the sum of 3 positive squares.
4254482 is the sum of 3 positive squares.
425448 is a divisor of 186718 - 1.
425448 in base 47 = 44S4 and consists of only the digits '4' and 'S'.

Thursday, February 2, 2017

Number of the day: 299096

Bartel Leendert van der Waerden was born on this day 114 years ago.

Properties of the number 299096:

299096 = 23 × 73 × 109 is the 273168th composite number and is not squarefree.
299096 has 3 distinct prime factors, 32 divisors, 13 antidivisors and 127008 totatives.
299096 has a semiprime digit sum 35 in base 10.
299096 = 747752 - 747732 = 373892 - 373852 = 106892 - 106752 = 53552 - 53272 = 15752 - 14772 = 8612 - 6652 = 7952 - 5772 = 5612 - 1252 is the difference of 2 nonnegative squares in 8 ways.
299096 = 362 + 1302 + 5302 is the sum of 3 positive squares.
2990962 = 1646402 + 2497042 is the sum of 2 positive squares in 1 way.
2990962 is the sum of 3 positive squares.
299096 is a divisor of 1936 - 1.
299096 = '29909' + '6' is the concatenation of 2 semiprime numbers.

The number 299096 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A204088: Row sums of A204087.

Wednesday, February 1, 2017

Number of the day: 50777603889348

John Napier was born on this day 467 years ago.

John Napier was born on this day 467 years ago.

Properties of the number 50777603889348:

50777603889348 = 22 × 3 × 7 × 17 × 79 × 733 × 614063 is composite and not squarefree.
50777603889348 has 7 distinct prime factors, 192 divisors, 107 antidivisors and 13463225837568 totatives.
Reversing the decimal digits of 50777603889348 results in a sphenic number.
50777603889348 is the difference of 2 nonnegative squares in 32 ways.
50777603889348 is the difference of 2 positive pentagonal numbers in 14 ways.
50777603889348 = 36642 + 149262 + 71258242 is the sum of 3 positive squares.
507776038893482 = 302359217445602 + 407940448227482 = 238953430067522 + 448037681376602 = 170331742442402 + 478355101562522 = 74815569168482 + 502234144881002 is the sum of 2 positive squares in 4 ways.
507776038893482 is the sum of 3 positive squares.
50777603889348 is a divisor of 15797368744 - 1.