Number of the day: 267018

Properties of the number 267018:

267018 = 2 × 3 × 191 × 233 is the 243621^th composite number and is squarefree.
267018 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 88160 totatives.
267018 = 11² + 76² + 511² is the sum of 3 positive squares.
267018² = 120330² + 238368² is the sum of 2 positive squares in 1 way.
267018² is the sum of 3 positive squares.
267018 is a proper divisor of 1153⁴⁰ - 1.
267018 is palindromic in (at least) the following bases: 65, and -69.

Number of the day: 88565

Properties of the number 88565:

88565 is a cyclic number.
88565 = 5 × 17713 is semiprime and squarefree.
88565 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 70848 totatives.
88565 = 44283² - 44282² = 8859² - 8854² is the difference of 2 nonnegative squares in 2 ways.
88565 is the difference of 2 positive pentagonal numbers in 2 ways.
88565 = 166² + 247² = 98² + 281² is the sum of 2 positive squares in 2 ways.
88565 = 23² + 40² + 294² is the sum of 3 positive squares.
88565² = 33453² + 82004² = 22440² + 85675² = 55076² + 69357² = 53139² + 70852² is the sum of 2 positive squares in 4 ways.
88565² is the sum of 3 positive squares.
88565 is a proper divisor of 1319⁵⁴ - 1.
88565 is an emirpimes in (at least) the following bases: 8, 13, 16, 18, 19, 20, 25, 26, 31, 32, 37, 40, 42, 43, 45, 49, 50, 53, 68, 72, 77, 81, 85, 86, 92, and 95.
88565 is palindromic in (at least) the following bases: 73, -56, and -77.
88565 in base 55 = TFF and consists of only the digits 'F' and 'T'.

The number 88565 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A251737: Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, U, I.

Number of the day: 2470

Properties of the number 2470:

2470 = 2 × 5 × 13 × 19 is the 2104^th composite number and is squarefree.
2470 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 864 totatives.
2470 has an emirp digit sum 13 in base 10.
2470 has a Fibonacci digit sum 13 in base 10.
2470 = 1² + … + 19² is the sum of at least 2 consecutive positive squares in 1 way.
2470 = (14 × 15)/2 + … + (25 × 26)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
2470 is the sum of 2 positive triangular numbers.
2470 is the difference of 2 positive pentagonal numbers in 4 ways.
2470 = 15² + 33² + 34² is the sum of 3 positive squares.
2470² = 1482² + 1976² = 608² + 2394² = 1254² + 2128² = 950² + 2280² is the sum of 2 positive squares in 4 ways.
2470² is the sum of 3 positive squares.
2470 is a proper divisor of 571² - 1.
2470 is palindromic in (at least) the following bases: 4, 15, 64, 94, and -22.
2470 in base 3 = 10101111 and consists of only the digits '0' and '1'.
2470 in base 4 = 212212 and consists of only the digits '1' and '2'.
2470 in base 8 = 4646 and consists of only the digits '4' and '6'.
2470 in base 9 = 3344 and consists of only the digits '3' and '4'.
2470 in base 15 = aea and consists of only the digits 'a' and 'e'.
2470 in base 49 = 11K and consists of only the digits '1' and 'K'.

The number 2470 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000330: Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.
A005598: a(n) = 1 + Sum_{i=1..n} (n-i+1)*phi(i).
A006918: a(n) = binomial(n+3, 3)/4, n odd; n(n+2)(n+4)/24, n even.
A020330: Numbers whose base 2 representation is the juxtaposition of two identical strings.
A035928: Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order.
A062744: Ninth column of triangle A062993 (without leading zeros). A Pfaff-Fuss or 10-Raney sequence.
A100157: Structured rhombic dodecahedral numbers (vertex structure 9).
A191724: Dispersion of A047218, (numbers >1 and congruent to 0 or 3 mod 5), by antidiagonals.
A249551: Numbers n such that there are precisely 8 groups of order n.
A299291: Coordination sequence for "ubt" 3D uniform tiling.

Number of the day: 64913

Properties of the number 64913:

64913 is a cyclic number.
64913 = 139 × 467 is semiprime and squarefree.
64913 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 64308 totatives.
64913 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 64913 results in an emirpimes.
64913 = 32457² - 32456² = 303² - 164² is the difference of 2 nonnegative squares in 2 ways.
64913 is the difference of 2 positive pentagonal numbers in 1 way.
64913 = 6² + 19² + 254² is the sum of 3 positive squares.
64913² is the sum of 3 positive squares.
64913 is a proper divisor of 1867⁴⁶ - 1.
64913 = '6491' + '3' is the concatenation of 2 prime numbers.
64913 is an emirpimes in (at least) the following bases: 2, 6, 7, 10, 11, 12, 16, 23, 26, 28, 29, 30, 31, 32, 34, 35, 37, 38, 39, 41, 44, 47, 53, 55, 58, 63, 64, 65, 67, 82, 87, 90, 91, 96, 98, 99, and 100.

The number 64913 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A095941: Number of subsets of {1,2,...,n} such that every number in the set is no larger than the sum of the other numbers in the set.
A104174: Numerator of the fractional part of a harmonic number.
A119520: The first 10 digits of the fifth root of n contain the digits 0-9.
A164470: Number of binary strings of length n with no substrings equal to 0001 0101 or 0111

Number of the day: 11618915159

Joseph-Louis Lagrange was born on this day 283 years ago.

Properties of the number 11618915159:

11618915159 is a cyclic number.
11618915159 = 61 × 5839 × 32621 is a sphenic number and squarefree.
11618915159 has 3 distinct prime factors, 8 divisors, 43 antidivisors and 11426133600 totatives.
11618915159 has a prime digit sum 47 in base 10.
Reversing the decimal digits of 11618915159 results in a sphenic number.
11618915159 = 5809457580² - 5809457579² = 95237040² - 95236979² = 997860² - 992021² = 194400² - 161779² is the difference of 2 nonnegative squares in 4 ways.
11618915159 is the difference of 2 positive pentagonal numbers in 4 ways.
11618915159 is not the sum of 3 positive squares.
11618915159² = 7489101400² + 8883273591² = 2095214209² + 11428441140² = 5648829609² + 10153320320² = 7387152460² + 8968231041² is the sum of 2 positive squares in 4 ways.
11618915159² is the sum of 3 positive squares.
11618915159 is a proper divisor of 1091⁵⁸³⁸⁰ - 1.
11618915159 = '11618' + '915159' is the concatenation of 2 sphenic numbers.

Number of the day: 41783

Properties of the number 41783:

41783 = 7 × 47 × 127 is a sphenic number and squarefree.
41783 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 34776 totatives.
41783 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 41783 results in a sphenic number.
41783 = 20892² - 20891² = 2988² - 2981² = 468² - 421² = 228² - 101² is the difference of 2 nonnegative squares in 4 ways.
41783 is the difference of 2 positive pentagonal numbers in 3 ways.
41783 is not the sum of 3 positive squares.
41783² is the sum of 3 positive squares.
41783 is a proper divisor of 659¹⁸ - 1.
41783 is palindromic in (at least) the following bases: -75, and -99.

The number 41783 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006722: Somos-6 sequence: a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = ... = a(5) = 1.
A101936: Numbers n with omega(n) = omega of 3 nearest larger and 3 nearest smaller neighbors.
A296198: Harary index of the n X n black bishop graph.
A296200: Harary index of the n X n white bishop graph.

Number of the day: 48478

David Hilbert was born on this day 157 years ago.

Properties of the number 48478:

48478 = 2 × 24239 is semiprime and squarefree.
48478 has 2 distinct prime factors, 4 divisors, 29 antidivisors and 24238 totatives.
48478 has an emirp digit sum 31 in base 10.
48478 is the difference of 2 positive pentagonal numbers in 2 ways.
48478 = 30² + 47² + 213² is the sum of 3 positive squares.
48478² is the sum of 3 positive squares.
48478 is a proper divisor of 3¹²¹¹⁹ - 1.
48478 is an emirpimes in (at least) the following bases: 2, 6, 7, 8, 9, 11, 13, 17, 20, 21, 23, 29, 31, 32, 33, 39, 41, 43, 44, 49, 54, 56, 60, 61, 64, 66, 67, 70, 85, 91, and 94.
48478 is palindromic in (at least) the following bases: 47, and 74.
48478 in base 47 = LiL and consists of only the digits 'L' and 'i'.
48478 in base 50 = JJS and consists of only the digits 'J' and 'S'.

The number 48478 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033456: LCM-convolution of squares A000290 with themselves.
A211630: Number of ordered triples (w,x,y) with all terms in {-n, ..., -1, 1, ..., n} and 5w + x + y > 0.

Number of the day: 65329012

Properties of the number 65329012:

65329012 = 2² × 7 × 2333179 is the 61470207^th composite number and is not squarefree.
65329012 has 3 distinct prime factors, 12 divisors, 25 antidivisors and 27998136 totatives.
65329012 has a triangular digit sum 28 in base 10.
65329012 = 16332254² - 16332252² = 2333186² - 2333172² is the difference of 2 nonnegative squares in 2 ways.
65329012 is the difference of 2 positive pentagonal numbers in 2 ways.
65329012 = 138² + 928² + 8028² is the sum of 3 positive squares.
65329012² is the sum of 3 positive squares.
65329012 is a proper divisor of 127⁸⁶⁴¹⁴ - 1.
65329012 = '6532901' + '2' is the concatenation of 2 prime numbers.

Number of the day: 959503

Properties of the number 959503:

959503 is a cyclic number.
959503 = 859 × 1117 is semiprime and squarefree.
959503 has 2 distinct prime factors, 4 divisors, 37 antidivisors and 957528 totatives.
959503 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 959503 results in an emirpimes.
959503 = 479752² - 479751² = 988² - 129² is the difference of 2 nonnegative squares in 2 ways.
959503 is the sum of 2 positive triangular numbers.
959503 is the difference of 2 positive pentagonal numbers in 1 way.
959503 is not the sum of 3 positive squares.
959503² = 201865² + 938028² is the sum of 2 positive squares in 1 way.
959503² is the sum of 3 positive squares.
959503 is a proper divisor of 23²³⁴ - 1.
959503 = '9' + '59503' is the concatenation of 2 semiprime numbers.
959503 is an emirpimes in (at least) the following bases: 2, 5, 9, 10, 13, 19, 21, 24, 37, 38, 41, 43, 46, 50, 51, 56, 57, 59, 62, 64, 65, 68, 72, 73, 76, 77, 79, 81, 84, 86, 90, 91, 95, 99, and 100.

Number of the day: 252354640

Properties of the number 252354640:

252354640 = 2⁴ × 5 × 3154433 is the 238553637^th composite number and is not squarefree.
252354640 has 3 distinct prime factors, 20 divisors, 15 antidivisors and 100941824 totatives.
252354640 has an emirp digit sum 31 in base 10.
252354640 = 63088661² - 63088659² = 31544332² - 31544328² = 15772169² - 15772161² = 12617737² - 12617727² = 6308876² - 6308856² = 3154453² - 3154413² is the difference of 2 nonnegative squares in 6 ways.
252354640 is the sum of 2 positive triangular numbers.
252354640 is the difference of 2 positive pentagonal numbers in 2 ways.
252354640 = 10728² + 11716² = 2936² + 15612² is the sum of 2 positive squares in 2 ways.
252354640 = 196² + 1920² + 15768² is the sum of 3 positive squares.
252354640² = 133087360² + 214407600² = 22174672² + 251378496² = 91673664² + 235114448² = 151412784² + 201883712² is the sum of 2 positive squares in 4 ways.
252354640² is the sum of 3 positive squares.
252354640 is a proper divisor of 1579¹⁵⁶¹⁶ - 1.

Number of the day: 824962

Properties of the number 824962:

824962 = 2 × 412481 is semiprime and squarefree.
824962 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 412480 totatives.
824962 has an emirp digit sum 31 in base 10.
824962 is the difference of 2 positive pentagonal numbers in 2 ways.
824962 = 601² + 681² is the sum of 2 positive squares in 1 way.
824962 = 63² + 128² + 897² is the sum of 3 positive squares.
824962² = 102560² + 818562² is the sum of 2 positive squares in 1 way.
824962² is the sum of 3 positive squares.
824962 is a proper divisor of 607¹²⁸⁹ - 1.
824962 = '8249' + '62' is the concatenation of 2 semiprime numbers.
824962 is an emirpimes in (at least) the following bases: 2, 3, 7, 12, 19, 21, 31, 34, 35, 36, 37, 38, 46, 53, 64, 69, 70, 73, 75, 78, 81, 82, 83, 86, 88, 90, 91, 95, and 98.

Number of the day: 1993706753

Properties of the number 1993706753:

1993706753 is a cyclic number.
1993706753 is the 97928773^th prime.
1993706753 has 25 antidivisors and 1993706752 totatives.
Reversing the decimal digits of 1993706753 results in a sphenic number.
1993706753 = 996853377² - 996853376² is the difference of 2 nonnegative squares in 1 way.
1993706753 is the difference of 2 positive pentagonal numbers in 1 way.
1993706753 = 13913² + 42428² is the sum of 2 positive squares in 1 way.
1993706753 = 603² + 890² + 44638² is the sum of 3 positive squares.
1993706753² = 1180601528² + 1606563615² is the sum of 2 positive squares in 1 way.
1993706753² is the sum of 3 positive squares.
1993706753 is a proper divisor of 43^62303336 - 1.
1993706753 = '199' + '3706753' is the concatenation of 2 emirps.
1993706753 is an emirp in (at least) the following bases: 8, 13, 16, 19, 20, 22, 40, 47, 48, 52, 67, 71, 81, and 89.

Number of the day: 827986

Properties of the number 827986:

827986 = 2 × 37 × 67 × 167 is the 761963^th composite number and is squarefree.
827986 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 394416 totatives.
827986 is the difference of 2 positive pentagonal numbers in 6 ways.
827986 = 16² + 111² + 903² is the sum of 3 positive squares.
827986² = 268536² + 783230² is the sum of 2 positive squares in 1 way.
827986² is the sum of 3 positive squares.
827986 is a proper divisor of 1669¹⁹⁸ - 1.
827986 = '8279' + '86' is the concatenation of 2 semiprime numbers.

Number of the day: 792810

Properties of the number 792810:

792810 = 2 × 3² × 5 × 23 × 383 is the 729385^th composite number and is not squarefree.
792810 has 5 distinct prime factors, 48 divisors, 31 antidivisors and 201696 totatives.
792810 is the sum of 2 positive triangular numbers.
792810 is the difference of 2 positive pentagonal numbers in 2 ways.
792810 = 64² + 95² + 883² is the sum of 3 positive squares.
792810² = 475686² + 634248² is the sum of 2 positive squares in 1 way.
792810² is the sum of 3 positive squares.
792810 is a proper divisor of 1531²² - 1.

Number of the day: 9686

Sofia Kovalevskaya was born on this day 169 years ago.

Properties of the number 9686:

9686 = 2 × 29 × 167 is a sphenic number and squarefree.
9686 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 4648 totatives.
9686 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 9686 results in a prime.
9686 is the difference of 2 positive pentagonal numbers in 1 way.
9686 = 9² + 14² + 97² is the sum of 3 positive squares.
9686² = 6680² + 7014² is the sum of 2 positive squares in 1 way.
9686² is the sum of 3 positive squares.
9686 is a proper divisor of 1669¹⁴ - 1.
9686 is palindromic in (at least) the following bases: 4, 26, 40, 47, and -13.
9686 in base 26 = e8e and consists of only the digits '8' and 'e'.
9686 in base 39 = 6EE and consists of only the digits '6' and 'E'.
9686 in base 40 = 626 and consists of only the digits '2' and '6'.
9686 in base 46 = 4QQ and consists of only the digits '4' and 'Q'.
9686 in base 47 = 4I4 and consists of only the digits '4' and 'I'.

The number 9686 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002838: Balancing weights on the integer line.
A076822: Number of partitions of the n-th triangular number involving only the numbers 1..n and with exactly n terms.
A115160: Numbers that are not the sum of two triangular numbers and a fourth power.
A188181: T(n,k)=Number of strictly increasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero
A198086: Number of isomorphism classes of nanocones with 5 pentagons and a symmetric boundary of length n.
A216635: T(n,k)=Number of nondecreasing arrays of n 0..n-1 integers with the sum of their k'th powers equal to sum(i^k,i=0..n-1)
A216645: T(n,k)=Number of nondecreasing arrays of n 1..n integers with the sum of their k powers equal to sum(i^k,i=1..n)
A234524: Numbers n such that A234519(n) = n.
A255684: Bernoulli number B_{n} has denominator 354.
A317160: T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

Number of the day: 16872

Alfred Tarski was born on this day 118 years ago.

Properties of the number 16872:

16872 = 2³ × 3 × 19 × 37 is the 14926^th composite number and is not squarefree.
16872 has 4 distinct prime factors, 32 divisors, 15 antidivisors and 5184 totatives.
Reversing the decimal digits of 16872 results in a sphenic number.
16872 = 4219² - 4217² = 2111² - 2107² = 1409² - 1403² = 709² - 697² = 241² - 203² = 151² - 77² = 149² - 73² = 131² - 17² is the difference of 2 nonnegative squares in 8 ways.
16872 is the sum of 2 positive triangular numbers.
16872 = 26² + 64² + 110² is the sum of 3 positive squares.
16872² = 5472² + 15960² is the sum of 2 positive squares in 1 way.
16872² is the sum of 3 positive squares.
16872 is a proper divisor of 1481² - 1.
16872 is palindromic in (at least) the following bases: 26, and -27.
16872 in base 26 = ooo and consists of only the digit 'o'.
16872 in base 31 = hh8 and consists of only the digits '8' and 'h'.
16872 in base 37 = CC0 and consists of only the digits '0' and 'C'.

The number 16872 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007290: a(n) = 2*binomial(n,3).
A064200: a(n) = 12*n*(n-1).
A127919: 1/3 of product of three numbers: the n-th prime, the previous number and the following number.
A157266: a(n) = 1728*n - 408.
A168061: Denominator of (n+3) / ((n+2) * (n+1) * n).
A195557: Numerators b(n) of Pythagorean approximations b(n)/a(n) to 1/3.
A195616: Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3.
A208287: T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically
A240735: Floor(6^n/(3+sqrt(3))^n).
A263466: Least k such that prime(n) is the smallest prime p for which k^2 + p^2 is also prime, or 0 if none.

Number of the day: 4734174

Properties of the number 4734174:

4734174 = 2 × 3 × 789029 is a sphenic number and squarefree.
4734174 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 1578056 totatives.
4734174 has a sphenic digit sum 30 in base 10.
4734174 has an oblong digit sum 30 in base 10.
4734174 is the sum of 2 positive triangular numbers.
4734174 is the difference of 2 positive pentagonal numbers in 2 ways.
4734174 = 178² + 203² + 2159² is the sum of 3 positive squares.
4734174² = 2096760² + 4244526² is the sum of 2 positive squares in 1 way.
4734174² is the sum of 3 positive squares.
4734174 is a proper divisor of 37¹⁹⁷²⁵⁷ - 1.
4734174 = '473' + '4174' is the concatenation of 2 semiprime numbers.

Number of the day: 386

Properties of the number 386:

386 = 2 × 193 is semiprime and squarefree.
386 has 2 distinct prime factors, 4 divisors, 3 antidivisors and 192 totatives.
386 has an emirp digit sum 17 in base 10.
386 has a Fibonacci digit product 144 in base 10.
386 has sum of divisors equal to 582 which is a sphenic number.
Reversing the decimal digits of 386 results in a prime.
386 = 9³ - 7³ is the difference of 2 positive cubes in 1 way.
386 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
386 = 5² + 19² is the sum of 2 positive squares in 1 way.
386 = 4² + 9² + 17² is the sum of 3 positive squares.
386² = 190² + 336² is the sum of 2 positive squares in 1 way.
386² is the sum of 3 positive squares.
386 is a proper divisor of 1543² - 1.
386 = '38' + '6' is the concatenation of 2 semiprime numbers.
386 is an emirpimes in (at least) the following bases: 5, 8, 9, 11, 14, 17, 19, 26, 28, 29, 31, 35, 41, 43, 47, 50, 51, 53, 55, 59, 61, 64, 68, 71, 73, 74, 77, 79, 83, 93, 98, and 100.
386 is palindromic in (at least) the following bases: 12, -16, -35, -55, and -77.
386 in base 12 = 282 and consists of only the digits '2' and '8'.
386 in base 19 = 116 and consists of only the digits '1' and '6'.

The number 386 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000127: Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes.
A000346: a(n) = 2^(2*n+1) - binomial(2*n+1, n+1).
A005574: Numbers k such that k^2 + 1 is prime.
A005897: a(n) = 6*n^2 + 2 for n > 0, a(0)=1.
A038593: Differences between positive cubes in 1, 2 or 3 ways: union of A014439, A014440 and A014441.
A051783: Numbers k such that 3^k + 2 is prime.
A069099: Centered heptagonal numbers.
A100484: Even semiprimes.
A161344: Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
A299259: Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 4.8.8 2D tiling (cf. A008576).

Number of the day: 69025

Properties of the number 69025:

69025 = 5² × 11 × 251 is the 62167^th composite number and is not squarefree.
69025 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 50000 totatives.
69025 has a semiprime digit sum 22 in base 10.
69025 = 34513² - 34512² = 6905² - 6900² = 3143² - 3132² = 1393² - 1368² = 655² - 600² = 263² - 12² is the difference of 2 nonnegative squares in 6 ways.
69025 is the difference of 2 positive pentagonal numbers in 5 ways.
69025 = 36² + 65² + 252² is the sum of 3 positive squares.
69025² = 41415² + 55220² = 19327² + 66264² is the sum of 2 positive squares in 2 ways.
69025² is the sum of 3 positive squares.
69025 is a proper divisor of 149¹⁰ - 1.
69025 = '6902' + '5' is the concatenation of 2 pentagonal numbers.
69025 is palindromic in (at least) the following bases: 67, and 71.

The number 69025 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050910: Pure 3-complexes on 8 nodes with n multiple 3-simplexes.
A115004: Main diagonal of array in A114999.
A126155: Symmetric triangle, read by rows of 2*n+1 terms, similar to triangle A008301.
A126157: Main diagonal and central terms of symmetric triangle A126155.
A285925: Number of ordered set partitions of [n] into ten blocks such that equal-sized blocks are ordered with increasing least elements.

Number of the day: 9106875

Properties of the number 9106875:

9106875 = 3² × 5⁴ × 1619 is the 8497757^th composite number and is not squarefree.
9106875 has 3 distinct prime factors, 30 divisors, 35 antidivisors and 4854000 totatives.
9106875 has a triangular digit sum 36 in base 10.
9106875 is the difference of 2 nonnegative squares in 15 ways.
9106875 is the difference of 2 positive pentagonal numbers in 4 ways.
9106875 = 19² + 65² + 3017² is the sum of 3 positive squares.
9106875² = 5464125² + 7285500² = 2549925² + 8742600² = 3205620² + 8524035² = 4895856² + 7678917² is the sum of 2 positive squares in 4 ways.
9106875² is the sum of 3 positive squares.
9106875 is a proper divisor of 1693³²³⁶ - 1.

Number of the day: 4551

Richard Courant was born on this day 131 years ago.

Properties of the number 4551:

4551 = 3 × 37 × 41 is a sphenic number and squarefree.
4551 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 2880 totatives.
4551 has an emirpimes digit sum 15 in base 10.
4551 has a triangular digit sum 15 in base 10.
4551 = 2276² - 2275² = 760² - 757² = 80² - 43² = 76² - 35² is the difference of 2 nonnegative squares in 4 ways.
4551 is the difference of 2 positive pentagonal numbers in 1 way.
4551 is not the sum of 3 positive squares.
4551² = 2385² + 3876² = 999² + 4440² = 495² + 4524² = 1476² + 4305² is the sum of 2 positive squares in 4 ways.
4551² is the sum of 3 positive squares.
4551 is a proper divisor of 739² - 1.
4551 = '4' + '551' is the concatenation of 2 semiprime numbers.
4551 is palindromic in (at least) the following bases: 7, 20, 50, 65, -70, and -91.
4551 in base 7 = 16161 and consists of only the digits '1' and '6'.
4551 in base 17 = fcc and consists of only the digits 'c' and 'f'.
4551 in base 20 = b7b and consists of only the digits '7' and 'b'.
4551 in base 25 = 771 and consists of only the digits '1' and '7'.
4551 in base 27 = 66f and consists of only the digits '6' and 'f'.
4551 in base 47 = 22d and consists of only the digits '2' and 'd'.
4551 in base 49 = 1hh and consists of only the digits '1' and 'h'.
4551 in base 50 = 1f1 and consists of only the digits '1' and 'f'.

The number 4551 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067707: a(n) = 3*n^2 + 12*n.
A069127: Centered 14-gonal numbers.
A096819: Exponents n such that 2^n-19 is prime.
A111117: Divisors of 10^15 - 1.
A114697: Expansion of (1+x+x^2)/((x-1)*(x+1)*(x^2+2*x-1)); a Pellian-related sequence.
A132310: a(n) = 3^n*Sum_{ k=0..n } binomial(2*k,k)/3^k.
A171271: Numbers n such that phi(n)=2*phi(n-1).
A216840: Smallest palindromic number of 3 digits in two bases differing by n.
A257352: G.f.: (1-2*x+51*x^2)/(1-x)^3.
A278177: T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.

Number of the day: 686338

Properties of the number 686338:

686338 = 2 × 343169 is semiprime and squarefree.
686338 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 343168 totatives.
686338 has a semiprime digit sum 34 in base 10.
686338 has a Fibonacci digit sum 34 in base 10.
686338 is the difference of 2 positive pentagonal numbers in 2 ways.
686338 = 463² + 687² is the sum of 2 positive squares in 1 way.
686338 = 40² + 183² + 807² is the sum of 3 positive squares.
686338² = 257600² + 636162² is the sum of 2 positive squares in 1 way.
686338² is the sum of 3 positive squares.
686338 is a proper divisor of 997²²⁴ - 1.
686338 is an emirpimes in (at least) the following bases: 2, 5, 11, 12, 16, 17, 22, 23, 24, 33, 34, 35, 41, 42, 47, 50, 55, 61, 64, 65, 68, 70, 76, 81, 91, 92, 94, and 98.
686338 is palindromic in (at least) base 99.

Number of the day: 3954

Properties of the number 3954:

3954 = 2 × 3 × 659 is a sphenic number and squarefree.
3954 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 1316 totatives.
3954 has a semiprime digit sum 21 in base 10.
3954 has a Fibonacci digit sum 21 in base 10.
3954 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 3954 results in a semiprime.
3954 is the sum of 2 positive triangular numbers.
3954 is the difference of 2 positive pentagonal numbers in 2 ways.
3954 = 8² + 13² + 61² is the sum of 3 positive squares.
3954² is the sum of 3 positive squares.
3954 is a proper divisor of 1319² - 1.
3954 = '395' + '4' is the concatenation of 2 semiprime numbers.
3954 is palindromic in (at least) the following bases: 18, 38, 59, -28, -52, and -67.
3954 in base 18 = c3c and consists of only the digits '3' and 'c'.
3954 in base 37 = 2WW and consists of only the digits '2' and 'W'.
3954 in base 38 = 2S2 and consists of only the digits '2' and 'S'.
3954 in base 58 = 1AA and consists of only the digits '1' and 'A'.
3954 in base 59 = 181 and consists of only the digits '1' and '8'.
3954 in base 62 = 11m and consists of only the digits '1' and 'm'.

The number 3954 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050414: Numbers n such that 2^n - 3 is prime.
A075649: Right side of the triangle A075652.
A090801: List of distinct numbers appearing as denominators of Bernoulli numbers.
A097030: Numbers in the cycle-attractors of length=14 if the function f(x)=A063919(x) is iterated; f(x) is the sum of unitary proper divisors.
A208945: T(n,k) = number of n-bead necklaces labeled with numbers -k..k not allowing reversal, with sum zero with no three beads in a row equal.
A227360: G.f.: 1/(1 - x*(1-x^3)/(1 - x^2*(1-x^4)/(1 - x^3*(1-x^5)/(1 - x^4*(1-x^6)/(1 - ...))))), a continued fraction.
A248549: Numbers n such that the smallest prime divisor of n^2+1 is 61.
A252433: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 4 6 or 7
A275190: Positions of 5 in A274640.
A280473: G.f.: Product_{i>=1, j>=1, k>=1} (1 + x^(i*j*k)).

Number of the day: 6886

Camille Jordan was born on this day 181 years ago.

Properties of the number 6886:

6886 = 2 × 11 × 313 is a sphenic number and squarefree.
6886 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 3120 totatives.
6886 has a triangular digit sum 28 in base 10.
6886 = 19³ + 3³ is the sum of 2 positive cubes in 1 way.
6886 is the difference of 2 positive pentagonal numbers in 2 ways.
6886 = 1² + 54² + 63² is the sum of 3 positive squares.
6886² = 550² + 6864² is the sum of 2 positive squares in 1 way.
6886² is the sum of 3 positive squares.
6886 is a proper divisor of 1277⁴ - 1.
6886 = '6' + '886' is the concatenation of 2 semiprime numbers.
6886 is a palindrome (in base 10).
6886 is palindromic in (at least) the following bases: 9, 25, 32, 81, -5, -9, -25, and -85.
6886 in base 3 = 100110001 and consists of only the digits '0' and '1'.
6886 consists of only the digits '6' and '8'.
6886 in base 24 = bmm and consists of only the digits 'b' and 'm'.
6886 in base 25 = b0b and consists of only the digits '0' and 'b'.
6886 in base 32 = 6n6 and consists of only the digits '6' and 'n'.
6886 in base 58 = 22g and consists of only the digits '2' and 'g'.

The number 6886 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005064: Sum of cubes of primes dividing n.
A029965: Palindromic in bases 9 and 10.
A072041: a(n) is the smallest number of the form k + reverse(k) for exactly n integers k, or -1 if no such number exists.
A086119: Numbers of the form p^3 + q^3, p, q primes.
A099165: Palindromic in bases 10 and 32.
A120398: Sums of two distinct prime cubes.
A179986: Second 9-gonal (or nonagonal) numbers: a(n) = n*(7*n+5)/2.
A220083: a(n) = (15*n^2 + 9*n + 2)/2.
A250410: Palindromic in bases 10 and 25.
A271635: Numbers n such that Bernoulli number B_{n} has denominator 138.

Number of the day: 475

Sir Isaac Newton was born on this day 376 years ago.

Properties of the number 475:

475 = 5² × 19 is the 383^th composite number and is not squarefree.
475 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 360 totatives.
Reversing the decimal digits of 475 results in a sphenic number.
475 = 238² - 237² = 50² - 45² = 22² - 3² is the difference of 2 nonnegative squares in 3 ways.
475 is the sum of 2 positive triangular numbers.
475 is the difference of 2 positive pentagonal numbers in 2 ways.
475 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
475 = 3² + 5² + 21² is the sum of 3 positive squares.
475² = 285² + 380² = 133² + 456² is the sum of 2 positive squares in 2 ways.
475² is the sum of 3 positive squares.
475 is a proper divisor of 151² - 1.
475 = '47' + '5' is the concatenation of 2 prime numbers.
475 is palindromic in (at least) the following bases: 24, 94, -10, and -79.
475 in base 3 = 122121 and consists of only the digits '1' and '2'.
475 in base 6 = 2111 and consists of only the digits '1' and '2'.
475 in base 8 = 733 and consists of only the digits '3' and '7'.
475 in base 9 = 577 and consists of only the digits '5' and '7'.
475 in base 12 = 337 and consists of only the digits '3' and '7'.
475 in base 21 = 11d and consists of only the digits '1' and 'd'.

The number 475 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005282: Mian-Chowla sequence (a B_2 sequence): a(1) = 1; for n>1, a(n) = smallest number > a(n-1) such that the pairwise sums of elements are all distinct.
A005728: Number of fractions in Farey series of order n.
A028560: a(n) = n*(n + 6), also numbers a(n) such that 9*(9 + a(n)) is a perfect square.
A061039: Numerator of 1/9 - 1/n^2.
A299267: Partial sums of A299266.
A301697: Coordination sequence for node of type V2 in "krj" 2-D tiling (or net).
A301712: Coordination sequence for node of type V1 in "usm" 2-D tiling (or net).
A301722: Coordination sequence for node of type V2 in "krb" 2-D tiling (or net).
A301726: Coordination sequence for node of type V2 in "kra" 2-D tiling (or net).
A304716: Number of integer partitions of n whose distinct parts are connected.

Number of the day: 6159728873

Properties of the number 6159728873:

6159728873 is a cyclic number.
6159728873 = 6397 × 962909 is semiprime and squarefree.
6159728873 has 2 distinct prime factors, 4 divisors, 55 antidivisors and 6158759568 totatives.
6159728873 has an oblong digit sum 56 in base 10.
6159728873 = 3079864437² - 3079864436² = 484653² - 478256² is the difference of 2 nonnegative squares in 2 ways.
6159728873 is the difference of 2 positive pentagonal numbers in 2 ways.
6159728873 = 47323² + 62612² = 41608² + 66547² is the sum of 2 positive squares in 2 ways.
6159728873 = 577² + 1362² + 78470² is the sum of 3 positive squares.
6159728873² = 2697277545² + 5537775152² = 544043585² + 6135656148² = 1680796215² + 5925975352² = 2197625380² + 5754363777² is the sum of 2 positive squares in 4 ways.
6159728873² is the sum of 3 positive squares.
6159728873 is a proper divisor of 691^2888724 - 1.
6159728873 = '615972887' + '3' is the concatenation of 2 prime numbers.
6159728873 = '61597' + '28873' is the concatenation of 2 semiprime numbers.
6159728873 = '615' + '9728873' is the concatenation of 2 sphenic numbers.
6159728873 is an emirpimes in (at least) the following bases: 5, 12, 17, 19, 24, 29, 30, 33, 35, 37, 41, 43, 44, 47, 49, 50, 54, 56, 57, 67, 70, 72, 73, 75, 76, 82, 85, 88, 90, and 91.

Number of the day: 69759

Properties of the number 69759:

69759 = 3² × 23 × 337 is the 62844^th composite number and is not squarefree.
69759 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 44352 totatives.
69759 has a triangular digit sum 36 in base 10.
69759 = 34880² - 34879² = 11628² - 11625² = 3880² - 3871² = 1528² - 1505² = 540² - 471² = 272² - 65² is the difference of 2 nonnegative squares in 6 ways.
69759 is the difference of 2 positive pentagonal numbers in 2 ways.
69759 is not the sum of 3 positive squares.
69759² = 36225² + 59616² is the sum of 2 positive squares in 1 way.
69759² is the sum of 3 positive squares.
69759 is a proper divisor of 1013⁴² - 1.
69759 = '6' + '9759' is the concatenation of 2 semiprime numbers.
69759 is palindromic in (at least) the following bases: 42, -59, -63, -90, and -93.
69759 in base 42 = dMd and consists of only the digits 'M' and 'd'.
69759 in base 62 = I99 and consists of only the digits '9' and 'I'.

The number 69759 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A193391: Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).

Number of the day: 2019

Happy New Year!

Properties of the number 2019:

2019 = 3 × 673 is semiprime and squarefree.
2019 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 1344 totatives.
2019 has an oblong digit sum 12 in base 10.
2019 = 1010² - 1009² = 338² - 335² is the difference of 2 nonnegative squares in 2 ways.
2019 is the sum of 2 positive triangular numbers.
2019 is the difference of 2 positive pentagonal numbers in 1 way.
2019 = 13² + 25² + 35² is the sum of 3 positive squares.
2019² = 1155² + 1656² is the sum of 2 positive squares in 1 way.
2019² is the sum of 3 positive squares.
2019 is a proper divisor of 929⁶ - 1.
2019 = '201' + '9' is the concatenation of 2 semiprime numbers.
2019 is an emirpimes in (at least) the following bases: 4, 6, 8, 11, 13, 23, 25, 29, 36, 40, 42, 44, 45, 46, 47, 51, 53, 55, 57, 63, 64, 65, 67, 69, 71, 75, 87, 91, 93, and 96.
2019 is palindromic in (at least) the following bases: 19, 24, -15, and -28.
2019 in base 19 = 5b5 and consists of only the digits '5' and 'b'.
2019 in base 23 = 3ii and consists of only the digits '3' and 'i'.
2019 in base 24 = 3c3 and consists of only the digits '3' and 'c'.
2019 in base 44 = 11d and consists of only the digits '1' and 'd'.

The number 2019 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A028878: a(n) = (n+3)^2 - 6.
A037015: Numbers n with property that, reading binary expansion of n from right to left, run lengths strictly increase.
A046254: a(1) = 4; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A075003: Floor[ concatenation of n+1 and n divided by 2 ].
A100037: Positions of occurrences of the natural numbers as second subsequence in A100035.
A100287: First occurrence of n in A100002; the least k such that A100002(k) = n.
A112558: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 4 multiples of n-1, n-2, ..., 1, for n>=1.
A113747: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 10 multiples of n-1, n-2, ..., 1, for n>=1.
A127423: a(1) = 1; for n>1, a(n) = n concatenated with n-1.
A201847: T(n,k)=Number of zero-sum nXk -1..1 arrays with every element equal to at least one horizontal or vertical neighbor