Number of the day: 28347

Carl Friedrich Gauss was born on this day 242 years ago.

Claude Shannon was born on this day 103 years ago.

Properties of the number 28347:

28347 = 3 × 11 × 859 is a sphenic number and squarefree.
28347 has 3 distinct prime factors, 8 divisors, 31 antidivisors and 17160 totatives.
28347 = 14174² - 14173² = 4726² - 4723² = 1294² - 1283² = 446² - 413² is the difference of 2 nonnegative squares in 4 ways.
28347 is the sum of 2 positive triangular numbers.
28347 is the difference of 2 positive pentagonal numbers in 2 ways.
28347 = 13² + 17² + 167² is the sum of 3 positive squares.
28347² is the sum of 3 positive squares.
28347 is a proper divisor of 1979⁶ - 1.
28347 = '283' + '47' is the concatenation of 2 prime numbers.
28347 is palindromic in (at least) the following bases: 2, 32, 41, 67, 74, -34, and -65.
28347 in base 32 = rlr and consists of only the digits 'l' and 'r'.
28347 in base 41 = GZG and consists of only the digits 'G' and 'Z'.
28347 in base 59 = 88R and consists of only the digits '8' and 'R'.

The number 28347 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023609: Convolution of Fibonacci numbers and composite numbers.
A047661: Row 5 of square array defined in A047662.
A066897: Total number of odd parts in all partitions of n.
A270694: Alternating sum of centered heptagonal pyramidal numbers.

Number of the day: 999541962

Henri Poincaré was born on this day 165 years ago.

Properties of the number 999541962:

999541962 = 2 × 3² × 17 × 3266477 is the 948716359^th composite number and is not squarefree.
999541962 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 313581696 totatives.
999541962 = 209³ + 393³ + 976³ is the sum of 3 positive cubes in 1 way.
999541962 is the difference of 2 positive pentagonal numbers in 2 ways.
999541962 = 16629² + 26889² = 2019² + 31551² is the sum of 2 positive squares in 2 ways.
999541962 = 59² + 640² + 31609² is the sum of 3 positive squares.
999541962² = 470372688² + 881948790² = 127402938² + 991389240² = 446494680² + 894274362² = 578950470² + 814800888² is the sum of 2 positive squares in 4 ways.
999541962² is the sum of 3 positive squares.
999541962 is a proper divisor of 179¹¹⁰⁷²⁸ - 1.
999541962 = '9995' + '41962' is the concatenation of 2 emirpimes.

Number of the day: 2462763

Kurt Gödel was born on this day 113 years ago.

Properties of the number 2462763:

2462763 = 3 × 820921 is semiprime and squarefree.
2462763 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 1641840 totatives.
2462763 has a sphenic digit sum 30 in base 10.
2462763 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 2462763 results in a sphenic number.
2462763 = 1231382² - 1231381² = 410462² - 410459² is the difference of 2 nonnegative squares in 2 ways.
2462763 is the difference of 2 positive pentagonal numbers in 1 way.
2462763 = 7² + 85² + 1567² is the sum of 3 positive squares.
2462763² = 1187637² + 2157480² is the sum of 2 positive squares in 1 way.
2462763² is the sum of 3 positive squares.
2462763 is a proper divisor of 149¹³⁶⁸² - 1.
2462763 = '2462' + '763' is the concatenation of 2 semiprime numbers.
2462763 is an emirpimes in (at least) the following bases: 6, 9, 13, 24, 27, 30, 33, 52, 60, 64, 76, 79, 89, 92, 96, and 97.

Number of the day: 503517

Properties of the number 503517:

503517 = 3 × 7 × 23977 is a sphenic number and squarefree.
503517 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 287712 totatives.
503517 has a semiprime digit sum 21 in base 10.
503517 has a Fibonacci digit sum 21 in base 10.
503517 has a triangular digit sum 21 in base 10.
503517 = 251759² - 251758² = 83921² - 83918² = 35969² - 35962² = 11999² - 11978² is the difference of 2 nonnegative squares in 4 ways.
503517 is the sum of 2 positive triangular numbers.
503517 is the difference of 2 positive pentagonal numbers in 2 ways.
503517 = 40² + 59² + 706² is the sum of 3 positive squares.
503517² = 331485² + 379008² is the sum of 2 positive squares in 1 way.
503517² is the sum of 3 positive squares.
503517 is a proper divisor of 1871¹² - 1.

Number of the day: 1828204

Properties of the number 1828204:

1828204 = 2² × 7 × 65293 is the 1691170^th composite number and is not squarefree.
1828204 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 783504 totatives.
1828204 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 1828204 results in a prime.
1828204 = 457052² - 457050² = 65300² - 65286² is the difference of 2 nonnegative squares in 2 ways.
1828204 is the difference of 2 positive pentagonal numbers in 2 ways.
1828204 = 58² + 258² + 1326² is the sum of 3 positive squares.
1828204² = 1239504² + 1343860² is the sum of 2 positive squares in 1 way.
1828204² is the sum of 3 positive squares.
1828204 is a proper divisor of 281⁵⁴⁴¹ - 1.

Number of the day: 60979

Felix Klein was born on this day 170 years ago.

Andrey Kolmogorov was born on this day 116 years ago.

Properties of the number 60979:

60979 = 17² × 211 is the 54833^th composite number and is not squarefree.
60979 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 57120 totatives.
60979 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 60979 results in a semiprime.
60979 = 30490² - 30489² = 1802² - 1785² = 250² - 39² is the difference of 2 nonnegative squares in 3 ways.
60979 is the sum of 2 positive triangular numbers.
60979 is the difference of 2 positive pentagonal numbers in 2 ways.
60979 = 83² + 117² + 201² is the sum of 3 positive squares.
60979² = 33971² + 50640² = 28696² + 53805² is the sum of 2 positive squares in 2 ways.
60979² is the sum of 3 positive squares.
60979 is a proper divisor of 829¹² - 1.
60979 is palindromic in (at least) base -46.
60979 in base 16 = ee33 and consists of only the digits '3' and 'e'.

The number 60979 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A050842: Numbers k such that 181*2^k-1 is prime.

Number of the day: 61462

Properties of the number 61462:

61462 = 2 × 79 × 389 is a sphenic number and squarefree.
61462 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 30264 totatives.
61462 has a prime digit sum 19 in base 10.
61462 is the sum of 2 positive triangular numbers.
61462 is the difference of 2 positive pentagonal numbers in 3 ways.
61462 = 1² + 90² + 231² is the sum of 3 positive squares.
61462² = 29862² + 53720² is the sum of 2 positive squares in 1 way.
61462² is the sum of 3 positive squares.
61462 is a proper divisor of 1423⁹⁷ - 1.
61462 = '614' + '62' is the concatenation of 2 semiprime numbers.
61462 is palindromic in (at least) base -14.

The number 61462 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A094377: Greatest number having exactly n representations as ab+ac+bc with 0 < a < b < c.

Number of the day: 887318

Properties of the number 887318:

887318 = 2 × 443659 is semiprime and squarefree.
887318 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 443658 totatives.
887318 has a semiprime digit sum 35 in base 10.
887318 = 18² + 95² + 937² is the sum of 3 positive squares.
887318² is the sum of 3 positive squares.
887318 is a proper divisor of 59⁷³⁹⁴³ - 1.
887318 is an emirpimes in (at least) the following bases: 4, 8, 9, 12, 15, 16, 21, 22, 23, 24, 25, 28, 29, 31, 36, 40, 54, 57, 58, 64, 65, 76, 77, 78, 80, 81, 84, 85, 88, 90, and 96.

Number of the day: 669

Properties of the number 669:

669 = 3 × 223 is semiprime and squarefree.
669 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 444 totatives.
669 has a semiprime digit sum 21 in base 10.
669 has a Fibonacci digit sum 21 in base 10.
669 has a triangular digit sum 21 in base 10.
669 = 335² - 334² = 113² - 110² is the difference of 2 nonnegative squares in 2 ways.
669 is the sum of 2 positive triangular numbers.
669 is the difference of 2 positive pentagonal numbers in 1 way.
669 = 10² + 13² + 20² is the sum of 3 positive squares.
669² is the sum of 3 positive squares.
669 is a proper divisor of 1783² - 1.
669 = '6' + '69' is the concatenation of 2 semiprime numbers.
669 is an emirpimes in (at least) the following bases: 3, 5, 11, 14, 17, 21, 22, 24, 25, 26, 27, 28, 31, 35, 37, 43, 44, 45, 48, 51, 53, 59, 60, 75, 78, 79, 85, 89, 92, 93, 94, and 99.
669 is palindromic in (at least) the following bases: -18, and -23.
669 in base 6 = 3033 and consists of only the digits '0' and '3'.
669 consists of only the digits '6' and '9'.
669 in base 11 = 559 and consists of only the digits '5' and '9'.
669 in base 25 = 11j and consists of only the digits '1' and 'j'.

The number 669 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001743: Every digit contains at least one loop (version 1).
A001748: 3 * primes.
A025147: Number of partitions of n into distinct parts >= 2.
A028505: Number of primes <= 100*n.
A051227: Bernoulli number B_{2n} has denominator 42.
A059729: Carryless squares n X n base 10.
A161345: Numbers k whose largest divisor <= sqrt(k) is 3.
A192065: Expansion of prod(k>=1, Q(x^k)^k ) where Q(x)=prod(k>=1, 1+x^k ).
A265072: Coordination sequence for (3,3,5) tiling of hyperbolic plane.
A298035: Coordination sequence of Dual(3.12.12) tiling with respect to a trivalent node.

Number of the day: 823417

Properties of the number 823417:

823417 is a cyclic number.
823417 = 7 × 79 × 1489 is a sphenic number and squarefree.
823417 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 696384 totatives.
823417 has a semiprime digit sum 25 in base 10.
823417 = 411709² - 411708² = 58819² - 58812² = 5251² - 5172² = 1021² - 468² is the difference of 2 nonnegative squares in 4 ways.
823417 is the difference of 2 positive pentagonal numbers in 4 ways.
823417 = 51² + 104² + 900² is the sum of 3 positive squares.
823417² = 381017² + 729960² is the sum of 2 positive squares in 1 way.
823417² is the sum of 3 positive squares.
823417 is a proper divisor of 1973⁷⁸ - 1.
823417 is palindromic in (at least) base -66.
823417 in base 3 = 1112211111221 and consists of only the digits '1' and '2'.

The number 823417 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A078679: Number of Grand Motzkin paths of length n with no zigzags, that is with no factors UDU and DUD.

Number of the day: 701525

Properties of the number 701525:

701525 = 5² × 11 × 2551 is the 644867^th composite number and is not squarefree.
701525 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 510000 totatives.
701525 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 701525 results in a semiprime.
701525 = 350763² - 350762² = 70155² - 70150² = 31893² - 31882² = 14043² - 14018² = 6405² - 6350² = 1413² - 1138² is the difference of 2 nonnegative squares in 6 ways.
701525 is the difference of 2 positive pentagonal numbers in 6 ways.
701525 = 32² + 135² + 826² is the sum of 3 positive squares.
701525² = 420915² + 561220² = 196427² + 673464² is the sum of 2 positive squares in 2 ways.
701525² is the sum of 3 positive squares.
701525 is a proper divisor of 1319³⁰ - 1.
701525 in base 19 = 57557 and consists of only the digits '5' and '7'.

Number of the day: 618247

Properties of the number 618247:

618247 is a cyclic number.
618247 = 7 × 88321 is semiprime and squarefree.
618247 has 2 distinct prime factors, 4 divisors, 35 antidivisors and 529920 totatives.
618247 has a triangular digit sum 28 in base 10.
618247 = 309124² - 309123² = 44164² - 44157² is the difference of 2 nonnegative squares in 2 ways.
618247 is the difference of 2 positive pentagonal numbers in 2 ways.
618247 is not the sum of 3 positive squares.
618247² = 148680² + 600103² is the sum of 2 positive squares in 1 way.
618247² is the sum of 3 positive squares.
618247 is a proper divisor of 1747⁶⁰ - 1.
618247 = '6' + '18247' is the concatenation of 2 semiprime numbers.
618247 is an emirpimes in (at least) the following bases: 2, 3, 7, 9, 19, 20, 21, 24, 25, 26, 29, 35, 39, 40, 44, 45, 47, 51, 53, 54, 63, 67, 70, 76, 79, 85, 89, 92, 94, and 96.
618247 is palindromic in (at least) base -97.

Number of the day: 88451

Properties of the number 88451:

88451 = 11² × 17 × 43 is the 79878^th composite number and is not squarefree.
88451 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 73920 totatives.
88451 has an emirpimes digit sum 26 in base 10.
88451 = 44226² - 44225² = 4026² - 4015² = 2610² - 2593² = 1050² - 1007² = 426² - 305² = 330² - 143² is the difference of 2 nonnegative squares in 6 ways.
88451 is the difference of 2 positive pentagonal numbers in 5 ways.
88451 = 1² + 51² + 293² is the sum of 3 positive squares.
88451² = 41624² + 78045² is the sum of 2 positive squares in 1 way.
88451² is the sum of 3 positive squares.
88451 is a proper divisor of 1291¹⁰ - 1.
88451 is palindromic in (at least) base 88.
88451 in base 17 = 11010 and consists of only the digits '0' and '1'.

The number 88451 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A063496: a(n) = (2*n-1)*(8*n^2-8*n+3)/3.
A100606: a(n) = n^4 + n^3 + n.
A197351: a(0)=0, a(1)=1, a(2n)=17*a(n), a(2n+1)=a(2n)+1.
A305412: a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).

Number of the day: 938249

Properties of the number 938249:

938249 is a cyclic number.
938249 = 13 × 72173 is semiprime and squarefree.
938249 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 866064 totatives.
938249 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 938249 results in an emirpimes.
938249 = 26³ + 33³ + 96³ = 20³ + 26³ + 97³ is the sum of 3 positive cubes in 2 ways.
938249 = 469125² - 469124² = 36093² - 36080² is the difference of 2 nonnegative squares in 2 ways.
938249 is the difference of 2 positive pentagonal numbers in 2 ways.
938249 = 340² + 907² = 35² + 968² is the sum of 2 positive squares in 2 ways.
938249 = 32² + 125² + 960² is the sum of 3 positive squares.
938249² = 360865² + 866076² = 67760² + 935799² = 616760² + 707049² = 297375² + 889876² is the sum of 2 positive squares in 4 ways.
938249² is the sum of 3 positive squares.
938249 is a proper divisor of 53¹⁸⁰⁴³ - 1.
938249 = '9' + '38249' is the concatenation of 2 semiprime numbers.
938249 is an emirpimes in (at least) the following bases: 4, 5, 8, 10, 15, 17, 19, 20, 21, 23, 35, 37, 38, 45, 51, 52, 62, 64, 65, 71, 77, 78, 80, 82, 85, 87, 88, 89, 91, 95, 97, and 100.

Number of the day: 3488

Leonhard Euler was born on this day 312 years ago.

Properties of the number 3488:

3488 = 2⁵ × 109 is the 3000^th composite number and is not squarefree.
3488 has 2 distinct prime factors, 12 divisors, 17 antidivisors and 1728 totatives.
3488 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 3488 results in a semiprime.
3488 = 873² - 871² = 438² - 434² = 222² - 214² = 117² - 101² is the difference of 2 nonnegative squares in 4 ways.
3488 = 28² + 52² is the sum of 2 positive squares in 1 way.
3488 = 16² + 36² + 44² is the sum of 3 positive squares.
3488² = 1920² + 2912² is the sum of 2 positive squares in 1 way.
3488² is the sum of 3 positive squares.
3488 is a proper divisor of 1153³ - 1.
3488 is palindromic in (at least) the following bases: 20, -27, -41, and -42.
3488 in base 20 = 8e8 and consists of only the digits '8' and 'e'.
3488 in base 26 = 544 and consists of only the digits '4' and '5'.
3488 in base 29 = 448 and consists of only the digits '4' and '8'.
3488 in base 41 = 233 and consists of only the digits '2' and '3'.

The number 3488 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033816: a(n) = 2*n^2 + 3*n + 3.
A068817: Numbers n such that n concatenated with n 1's is a prime.
A121207: Triangle read by rows. The definition is by diagonals. The r-th diagonal from the right, for r >= 0, is given by b(0) = b(1) = 1; b(n+1) = Sum_{k=0..n} binomial(n+2,k+r)*a(k).
A124496: Triangle read by rows: T(n,k) is the number of set partitions of {1,2,...,n} in which the size of the last block is k, 1<=k<=n; the blocks are ordered with increasing least elements.
A154493: a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(0)=1,a(1)=4.
A178740: Product of the 5th power of a prime (A050997) and a different prime (p^5*q).
A260047: Composites whose prime factorization in base 3 is an anagram of the number in base 3.
A271634: Numbers n such that Bernoulli number B_{n} has denominator 510.
A299380: Numbers n such that n * 17^n - 1 is prime.
A316466: a(n) = 2*n*(7*n - 3).

Number of the day: 3927

Properties of the number 3927:

3927 = 3 × 7 × 11 × 17 is the 3382^th composite number and is squarefree.
3927 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 1920 totatives.
3927 has a semiprime digit sum 21 in base 10.
3927 has a Fibonacci digit sum 21 in base 10.
3927 has a triangular digit sum 21 in base 10.
3927 has a triangular digit product 378 in base 10.
3927 = 1964² - 1963² = 656² - 653² = 284² - 277² = 184² - 173² = 124² - 107² = 104² - 83² = 76² - 43² = 64² - 13² is the difference of 2 nonnegative squares in 8 ways.
3927 is the difference of 2 positive pentagonal numbers in 2 ways.
3927 is not the sum of 3 positive squares.
3927² = 1848² + 3465² is the sum of 2 positive squares in 1 way.
3927² is the sum of 3 positive squares.
3927 is a proper divisor of 307² - 1.
3927 is palindromic in (at least) the following bases: 6, 36, 76, and -6.
3927 in base 4 = 331113 and consists of only the digits '1' and '3'.
3927 in base 12 = 2333 and consists of only the digits '2' and '3'.
3927 in base 35 = 377 and consists of only the digits '3' and '7'.
3927 in base 36 = 313 and consists of only the digits '1' and '3'.
3927 in base 62 = 11L and consists of only the digits '1' and 'L'.

The number 3927 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006190: a(n) = 3*a(n-1) + a(n-2), with a(0)=0, a(1)=1.
A024966: 7 times triangular numbers: 7*n*(n+1)/2.
A026907: Triangular array T read by rows (9-diamondization of Pascal's triangle). Step 1: t(n,k) = sum of 9 entries in diamond-shaped subarray of Pascal's triangle having vertices C(n,k), C(n+4,k+2), C(n+2,k), C(n+2,k+2). Step 2: T(n,k) = t(n,k) - t(0,0) + 1.
A033568: Second pentagonal numbers with odd index: (2*n-1)*(3*n-1).
A089558: a(n)=A089551(n)/2.
A132355: Numbers of the form 9*h^2 + 2*h, for h an integer.
A138940: Indices n such that A019328(n) = Phi(n,10) is prime, where Phi is a cyclotomic polynomial.
A250676: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction
A266055: T(n,k)=Number of nXk integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than or equal to itself.
A324315: Squarefree integers m > 1 such that if prime p divides m, then the sum of the base p digits of m is at least p.

Number of the day: 36437343601

Properties of the number 36437343601:

36437343601 is a cyclic number.
36437343601 = 17 × 4441 × 482633 is a sphenic number and squarefree.
36437343601 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 34286177280 totatives.
Reversing the decimal digits of 36437343601 results in a sphenic number.
36437343601 = 18218671801² - 18218671800² = 1071686585² - 1071686568² = 4104601² - 4100160² = 279065² - 203568² is the difference of 2 nonnegative squares in 4 ways.
36437343601 is the difference of 2 positive pentagonal numbers in 4 ways.
36437343601 = 84175² + 171324² = 40476² + 186545² = 123500² + 145551² = 6351² + 190780² is the sum of 2 positive squares in 4 ways.
36437343601 = 2691² + 5686² + 190782² is the sum of 3 positive squares.
36437343601² = 17146985224² + 32150597295² = 6537263985² + 35846118176² = 14540767024² + 33410269425² = 15101190840² + 33160730449² = 8767915151² + 35366702880² = 22266482351² + 28842395400² = 24485724401² + 26983871280² = 2423287560² + 36356673199² = 5932843601² + 35951097000² = 14970827776² + 33219788145² = 8906758575² + 35331992024² = 22153025295² + 28929629776² = 22636935599² + 28552568280² is the sum of 2 positive squares in 13 ways.
36437343601² is the sum of 3 positive squares.
36437343601 is a proper divisor of 1543¹¹⁸⁶⁸⁰ - 1.

Number of the day: 7883603282

Properties of the number 7883603282:

7883603282 = 2 × 31177 × 126433 is a sphenic number and squarefree.
7883603282 has 3 distinct prime factors, 8 divisors, 71 antidivisors and 3941644032 totatives.
7883603282 has a prime digit sum 47 in base 10.
Reversing the decimal digits of 7883603282 results in a sphenic number.
7883603282 = 59891² + 65549² = 28501² + 84091² is the sum of 2 positive squares in 2 ways.
7883603282 = 404² + 1315² + 88779² is the sum of 3 positive squares.
7883603282² = 4793355182² + 6258989280² = 3805127568² + 6904506130² = 709739520² + 7851590318² = 3168082032² + 7219034350² is the sum of 2 positive squares in 4 ways.
7883603282² is the sum of 3 positive squares.
7883603282 is a proper divisor of 787¹²⁴⁷⁰⁴ - 1.
7883603282 = '78' + '83603282' is the concatenation of 2 sphenic numbers.

Number of the day: 14610

Élie Joseph Cartan was born on this day 150 years ago.

Properties of the number 14610:

14610 = 2 × 3 × 5 × 487 is the 12899^th composite number and is squarefree.
14610 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 3888 totatives.
14610 has an oblong digit sum 12 in base 10.
14610 is the sum of 2 positive triangular numbers.
14610 is the difference of 2 positive pentagonal numbers in 2 ways.
14610 = 7² + 20² + 119² is the sum of 3 positive squares.
14610² = 8766² + 11688² is the sum of 2 positive squares in 1 way.
14610² is the sum of 3 positive squares.
14610 is a proper divisor of 1949² - 1.
14610 = '146' + '10' is the concatenation of 2 semiprime numbers.
14610 is palindromic in (at least) the following bases: 83, -40, -67, and -88.
14610 in base 33 = ddo and consists of only the digits 'd' and 'o'.

The number 14610 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032302: G.f.: Product_{k>=1} (1 + 2*x^k).
A065759: For a number n of length l, let f(n) be the sum of the products of the first i digits of x multiplied by the last l-i digits, for i from 1 to l-1, e.g., f(1234) = 1*234 + 12*34 + 123*4 = 1134. Sequence gives n such that f(n) = n.
A095694: T(n,3) diagonal of triangle in A095693.
A098845: Numbers k such that 4^k - 2^k - 1 is prime.
A138938: Indices k such that A019326(k)=Phi[k](8) is prime, where Phi is a cyclotomic polynomial.
A151801: Number of n X n binary arrays with rows, considered as binary numbers, in strictly increasing order, and columns, considered as binary numbers, in nondecreasing order.
A173303: Row sums of triangle A173302.
A175523: a(n)=a(n-1)+ p, where p is the least prime whose first digit equals the first digit of a(n-1) and p>=a(n-1)
A218628: Number of partitions of n+7 with largest inscribed rectangle having area <= n.
A265737: Consider any concatenation of the type n = concat(a,b). Sequence lists numbers that are the sum of the products of some of such couples a and b.

Number of the day: 5229

Properties of the number 5229:

5229 = 3² × 7 × 83 is the 4534^th composite number and is not squarefree.
5229 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 2952 totatives.
5229 = 2615² - 2614² = 873² - 870² = 377² - 370² = 295² - 286² = 135² - 114² = 73² - 10² is the difference of 2 nonnegative squares in 6 ways.
5229 is the sum of 2 positive triangular numbers.
5229 is the difference of 2 positive pentagonal numbers in 1 way.
5229 = 5² + 50² + 52² is the sum of 3 positive squares.
5229² is the sum of 3 positive squares.
5229 is a proper divisor of 499³ - 1.
5229 = '5' + '229' is the concatenation of 2 prime numbers.
5229 is palindromic in (at least) the following bases: 39, and 82.
5229 in base 17 = 111a and consists of only the digits '1' and 'a'.
5229 in base 29 = 669 and consists of only the digits '6' and '9'.
5229 in base 38 = 3NN and consists of only the digits '3' and 'N'.
5229 in base 39 = 3H3 and consists of only the digits '3' and 'H'.

The number 5229 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026049: a(n) = dot_product(1,2,...,n)*(7,8,...,n,1,2,3,4,5,6).
A057949: Numbers with more than one factorization into S-primes. See A054520 and A057948 for definition.
A057950: Numbers primitive with respect to having more than one factorization into S-primes. See related sequences for definition.
A067603: Least k such that the GCD( prime(k)+1, prime(k+1)+1 ) = 2n.
A074346: a(1) = 10; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A075645: Sums of groups in A075643.
A115921: Numbers n such that the decimal digits of phi(n) are a permutation of those of n.
A194270: D-toothpick sequence of the second kind (see Comments lines for definition).
A295990: Numbers n such that there are precisely 4 groups of orders n and n + 1.
A299254: Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^4.6 2D tiling (cf. A250120).

Number of the day: 5203

Properties of the number 5203:

5203 = 11² × 43 is the 4510^th composite number and is not squarefree.
5203 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 4620 totatives.
5203 has a semiprime digit sum 10 in base 10.
5203 has a triangular digit sum 10 in base 10.
5203 has sum of divisors equal to 5852 which is an oblong number.
5203 = 2602² - 2601² = 242² - 231² = 82² - 39² is the difference of 2 nonnegative squares in 3 ways.
5203 is the sum of 2 positive triangular numbers.
5203 is the difference of 2 positive pentagonal numbers in 3 ways.
5203 = 3² + 35² + 63² is the sum of 3 positive squares.
5203² is the sum of 3 positive squares.
5203 is a proper divisor of 1291⁵ - 1.
5203 is palindromic in (at least) the following bases: 7, 40, -22, and -50.
5203 in base 7 = 21112 and consists of only the digits '1' and '2'.
5203 in base 17 = 1101 and consists of only the digits '0' and '1'.
5203 in base 18 = g11 and consists of only the digits '1' and 'g'.
5203 in base 21 = bgg and consists of only the digits 'b' and 'g'.
5203 in base 25 = 883 and consists of only the digits '3' and '8'.
5203 in base 39 = 3GG and consists of only the digits '3' and 'G'.
5203 in base 40 = 3A3 and consists of only the digits '3' and 'A'.
5203 in base 41 = 33b and consists of only the digits '3' and 'b'.

The number 5203 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045940: Numbers n such that the factorizations of n through n+3 have the same number of primes (including multiplicities).
A098547: a(n) = n^3 + n^2 + 1.
A124057: Numbers n such that n, n+1, n+2 and n+3 are products of exactly 3 primes.
A126230: Odd interprimes divisible by 11.
A165463: Numbers of the form 12n+7 for which Sum_{i=0..(4n+2)} J(i,12n+7) = 0, where J(i,m) is the Jacobi symbol.
A182260: Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w<x+y.
A195047: Concentric 17-gonal numbers.
A217725: Numbers n such that 5n is a partition number.
A219051: Numbers n such that 3^n - 34 is prime.
A232467: Triangle read by rows: T(n,k) = number of fully connected (n,k) corner designs (n >= 0, 1 <= k <= n+1).

Number of the day: 7978

Properties of the number 7978:

7978 = 2 × 3989 is semiprime and squarefree.
7978 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 3988 totatives.
7978 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 7978 results in an emirpimes.
7978 is the difference of 2 positive pentagonal numbers in 2 ways.
7978 = 33² + 83² is the sum of 2 positive squares in 1 way.
7978 = 3² + 20² + 87² is the sum of 3 positive squares.
7978² = 5478² + 5800² is the sum of 2 positive squares in 1 way.
7978² is the sum of 3 positive squares.
7978 is a proper divisor of 29⁹⁹⁷ - 1.
7978 is an emirpimes in (at least) the following bases: 3, 4, 8, 10, 11, 14, 15, 19, 23, 25, 26, 27, 28, 30, 33, 34, 37, 41, 47, 50, 52, 53, 55, 56, 60, 62, 66, 68, 73, 74, 76, 77, 80, 81, 82, 85, 88, 89, 91, 92, and 96.
7978 is palindromic in (at least) the following bases: -21, and -55.
7978 in base 20 = jii and consists of only the digits 'i' and 'j'.
7978 in base 51 = 33M and consists of only the digits '3' and 'M'.

The number 7978 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031418: Numbers n such that continued fraction for sqrt(n) has odd period and a pair of central terms both equal to 5.
A036063: Increasing gaps among twin primes: size.
A041334: Numerators of continued fraction convergents to sqrt(181).
A057968: Triangle T(n,k) of numbers of minimal 5-covers of an unlabeled n+5-set that cover k points of that set uniquely (k=5,..,n+5).
A107853: G.f. x*(x-1)*(x+1)^3/((2*x^3+x^2-1)*(x^4+1)).
A152231: Similar to A072921 but starting with 2.
A224492: Smallest k such that k*2*p(n)^2-1=q is prime, k*2*q^2-1=r, k*2*r^2-1=s, k*2*r^2-1=t, r, s, and t are also prime.
A239469: Number of 3-separable partitions of n; see Comments.
A284068: Numbers whose smallest decimal digit is 7.
A304834: a(n) = 36*n^2 - 8*n - 2 (n >=1).

Number of the day: 53275

Properties of the number 53275:

53275 = 5² × 2131 is the 47840^th composite number and is not squarefree.
53275 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 42600 totatives.
53275 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 53275 results in a semiprime.
53275 = 26638² - 26637² = 5330² - 5325² = 1078² - 1053² is the difference of 2 nonnegative squares in 3 ways.
53275 is the sum of 2 positive triangular numbers.
53275 is the difference of 2 positive pentagonal numbers in 3 ways.
53275 = 33² + 65² + 219² is the sum of 3 positive squares.
53275² = 31965² + 42620² = 14917² + 51144² is the sum of 2 positive squares in 2 ways.
53275² is the sum of 3 positive squares.
53275 is a proper divisor of 397²⁰ - 1.
53275 is palindromic in (at least) the following bases: 47, -38, -66, and -92.
53275 in base 39 = Z11 and consists of only the digits '1' and 'Z'.
53275 in base 47 = O5O and consists of only the digits '5' and 'O'.

The number 53275 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A150036: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}
A228261: Number of third differences of arrays of length 5 of numbers in 0..n.

Number of the day: 24501

Properties of the number 24501:

24501 = 3 × 8167 is semiprime and squarefree.
24501 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 16332 totatives.
24501 has an oblong digit sum 12 in base 10.
24501 = 12251² - 12250² = 4085² - 4082² is the difference of 2 nonnegative squares in 2 ways.
24501 is the sum of 2 positive triangular numbers.
24501 is the difference of 2 positive pentagonal numbers in 1 way.
24501 = 44² + 49² + 142² is the sum of 3 positive squares.
24501² is the sum of 3 positive squares.
24501 is a proper divisor of 7¹³⁶¹ - 1.
24501 is an emirpimes in (at least) the following bases: 3, 6, 9, 18, 24, 25, 26, 27, 37, 39, 46, 48, 49, 66, 69, 71, 73, 75, 85, 86, 91, 96, and 97.
24501 is palindromic in (at least) the following bases: 34, 52, and -69.
24501 in base 34 = l6l and consists of only the digits '6' and 'l'.
24501 in base 49 = AA1 and consists of only the digits '1' and 'A'.
24501 in base 51 = 9LL and consists of only the digits '9' and 'L'.
24501 in base 52 = 939 and consists of only the digits '3' and '9'.

The number 24501 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022802: a(n) = L(n+1) + c(n) where L(K) = k-th Lucas number and c(n) is n-th number that is 1 or not a Lucas number.
A023489: Sum of n-th Lucas number greater than 3 and n-th number that is 1 or is not a Fibonacci number.
A023495: a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th nonLucas number).
A026911: T(2n,n-2), T given by A026907.
A035548: Number of partitions of n with equal nonzero number of parts congruent to each of 0 and 3 (mod 4)
A115708: Semiprimes (A001358) whose digit reversal is a pentagonal number (A000326).
A126343: Triangle, read by rows, of the limit of coefficients of q in {[x^m] W(x,q)} as m grows when arranged into a triangle where row n is multiplied by n! for n>=1.
A158493: a(n) = 20*n^2 + 1.
A212707: Semiprimes of the form 5*n^2 + 1.
A221995: Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,4,6,4,1

Number of the day: 382673

Properties of the number 382673:

382673 is a cyclic number.
382673 = 257 × 1489 is semiprime and squarefree.
382673 has 2 distinct prime factors, 4 divisors, 39 antidivisors and 380928 totatives.
382673 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 382673 results in a prime.
382673 = 191337² - 191336² = 873² - 616² is the difference of 2 nonnegative squares in 2 ways.
382673 is the sum of 2 positive triangular numbers.
382673 is the difference of 2 positive pentagonal numbers in 2 ways.
382673 = 353² + 508² = 287² + 548² is the sum of 2 positive squares in 2 ways.
382673 = 9² + 56² + 616² is the sum of 3 positive squares.
382673² = 133455² + 358648² = 47648² + 379695² = 217935² + 314552² = 177073² + 339240² is the sum of 2 positive squares in 4 ways.
382673² is the sum of 3 positive squares.
382673 is a proper divisor of 1289²⁴ - 1.
382673 is an emirpimes in (at least) the following bases: 7, 9, 11, 12, 14, 18, 19, 21, 22, 25, 26, 27, 32, 34, 35, 39, 41, 42, 49, 55, 56, 58, 59, 62, 64, 65, 66, 68, 69, 70, 76, 77, 78, 80, 81, 87, 89, 94, 96, 97, 98, and 99.
382673 is palindromic in (at least) the following bases: 88, and 92.
382673 in base 50 = 333N and consists of only the digits '3' and 'N'.

Number of the day: 557917

Paul Cohen was born on this day 85 years ago.

Properties of the number 557917:

557917 is a cyclic number.
557917 = 673 × 829 is semiprime and squarefree.
557917 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 556416 totatives.
557917 has a semiprime digit sum 34 in base 10.
557917 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 557917 results in a sphenic number.
557917 = 278959² - 278958² = 751² - 78² is the difference of 2 nonnegative squares in 2 ways.
557917 is the difference of 2 positive pentagonal numbers in 1 way.
557917 = 501² + 554² = 94² + 741² is the sum of 2 positive squares in 2 ways.
557917 = 22² + 147² + 732² is the sum of 3 positive squares.
557917² = 319165² + 457608² = 139308² + 540245² = 55915² + 555108² = 363420² + 423317² is the sum of 2 positive squares in 4 ways.
557917² is the sum of 3 positive squares.
557917 is a proper divisor of 347⁷² - 1.
557917 = '5' + '57917' is the concatenation of 2 prime numbers.
557917 is an emirpimes in (at least) the following bases: 2, 4, 6, 11, 13, 19, 28, 31, 34, 35, 36, 38, 44, 49, 50, 51, 54, 63, 69, 75, 76, 79, 81, 86, 91, 92, 95, and 100.
557917 is palindromic in (at least) the following bases: 87, and -96.

Number of the day: 772836237802

Sophie Germain was born on this day 243 years ago.

Alexander Craig Aitken was born on this day 124 years ago.

Properties of the number 772836237802:

772836237802 = 2 × 10589 × 36492409 is a sphenic number and squarefree.
772836237802 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 386381615904 totatives.
772836237802 has a semiprime digit sum 55 in base 10.
772836237802 has a Fibonacci digit sum 55 in base 10.
772836237802 has a triangular digit sum 55 in base 10.
Reversing the decimal digits of 772836237802 results in a sphenic number.
772836237802 is the difference of 2 positive pentagonal numbers in 2 ways.
772836237802 = 465841² + 745539² = 161929² + 864069² is the sum of 2 positive squares in 2 ways.
772836237802 = 141² + 260² + 879111² is the sum of 3 positive squares.
772836237802² = 523243151760² + 568763970902² = 279835658202² + 720394235720² = 338820563240² + 694605266598² = 281794382298² + 719630305480² is the sum of 2 positive squares in 4 ways.
772836237802² is the sum of 3 positive squares.
772836237802 is a proper divisor of 17^4637544 - 1.