Number of the day: 8307

Carl Ludwig Siegel was born on this day 121 years ago.

Properties of the number 8307:

8307 = 3² × 13 × 71 is the 7264^th composite number and is not squarefree.
8307 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 5040 totatives.
8307 = 19² + … + 31² is the sum of at least 2 consecutive positive squares in 1 way.
8307 = 4154² - 4153² = 1386² - 1383² = 466² - 457² = 326² - 313² = 126² - 87² = 94² - 23² is the difference of 2 nonnegative squares in 6 ways.
8307 is the difference of 2 positive pentagonal numbers in 1 way.
8307 = 1² + 5² + 91² is the sum of 3 positive squares.
8307² = 3195² + 7668² is the sum of 2 positive squares in 1 way.
8307² is the sum of 3 positive squares.
8307 is a proper divisor of 1279⁴ - 1.
8307 is palindromic in (at least) the following bases: 48, 55, and -26.
8307 in base 25 = d77 and consists of only the digits '7' and 'd'.
8307 in base 45 = 44R and consists of only the digits '4' and 'R'.
8307 in base 47 = 3ZZ and consists of only the digits '3' and 'Z'.
8307 in base 48 = 3T3 and consists of only the digits '3' and 'T'.
8307 in base 52 = 33d and consists of only the digits '3' and 'd'.
8307 in base 54 = 2jj and consists of only the digits '2' and 'j'.
8307 in base 55 = 2f2 and consists of only the digits '2' and 'f'.

The number 8307 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006875: Non-seed mu-atoms of period n in Mandelbrot set.
A022103: Fibonacci sequence beginning 1, 13.
A031431: Least term in period of continued fraction for sqrt(n) is 7.
A056078: Number of proper T_1-hypergraphs with 3 labeled nodes and n hyperedges.
A136376: a(n) = n*F(n) + (n-1)*F(n-1).
A157365: 49n^2 + 2n.
A218563: Numbers n such that n^2 + 1 is divisible by a 4th power.
A218564: Numbers n such that n^2 + 1 is divisible by a 5th power.
A241744: Number of partitions p of n such that (number of numbers in p of form 3k) = (number of numbers in p of form 3k+1).
A252407: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 2 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 2 3 4 6 or 7

Number of the day: 93149

Properties of the number 93149:

93149 = 7² × 1901 is the 84151^th composite number and is not squarefree.
93149 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 79800 totatives.
93149 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 93149 results in a semiprime.
93149 = 46575² - 46574² = 6657² - 6650² = 975² - 926² is the difference of 2 nonnegative squares in 3 ways.
93149 is the difference of 2 positive pentagonal numbers in 3 ways.
93149 = 182² + 245² is the sum of 2 positive squares in 1 way.
93149 = 2² + 27² + 304² is the sum of 3 positive squares.
93149² = 26901² + 89180² is the sum of 2 positive squares in 1 way.
93149² is the sum of 3 positive squares.
93149 is a proper divisor of 883⁹⁵ - 1.
93149 = '9' + '3149' is the concatenation of 2 semiprime numbers.
93149 is palindromic in (at least) the following bases: 47, and -62.
93149 in base 47 = g7g and consists of only the digits '7' and 'g'.
93149 in base 61 = P22 and consists of only the digits '2' and 'P'.

Number of the day: 791281

Properties of the number 791281:

791281 is a cyclic number.
791281 = 647 × 1223 is semiprime and squarefree.
791281 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 789412 totatives.
791281 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 791281 results in an emirpimes.
791281 = 25³ + 36³ + 90³ is the sum of 3 positive cubes in 1 way.
791281 = 395641² - 395640² = 935² - 288² is the difference of 2 nonnegative squares in 2 ways.
791281 is the sum of 2 positive triangular numbers.
791281 is the difference of 2 positive pentagonal numbers in 1 way.
791281 = 109² + 150² + 870² is the sum of 3 positive squares.
791281² is the sum of 3 positive squares.
791281 is a proper divisor of 179¹⁵⁹⁸ - 1.
791281 is an emirpimes in (at least) the following bases: 2, 3, 6, 10, 13, 15, 23, 24, 25, 26, 27, 30, 31, 33, 39, 41, 43, 44, 46, 49, 50, 54, 61, 63, 69, 76, 81, 84, 85, 88, 92, 93, 94, 95, 96, 98, and 99.
791281 is palindromic in (at least) base 28.
791281 in base 28 = 18181 and consists of only the digits '1' and '8'.

Number of the day: 47643

John von Neumann was born on this day 114 years ago.

Properties of the number 47643:

47643 is a cyclic number.
47643 = 3 × 15881 is semiprime and squarefree.
47643 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 31760 totatives.
47643 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 47643 results in a sphenic number.
47643 = 23822² - 23821² = 7942² - 7939² is the difference of 2 nonnegative squares in 2 ways.
47643 is the sum of 2 positive triangular numbers.
47643 is the difference of 2 positive pentagonal numbers in 1 way.
47643 = 5² + 23² + 217² is the sum of 3 positive squares.
47643² = 12000² + 46107² is the sum of 2 positive squares in 1 way.
47643² is the sum of 3 positive squares.
47643 is a proper divisor of 1933⁴⁰ - 1.
47643 = '47' + '643' is the concatenation of 2 prime numbers.
47643 is an emirpimes in (at least) the following bases: 3, 6, 8, 9, 15, 16, 21, 33, 34, 37, 41, 47, 51, 53, 60, 69, 78, 80, 81, 89, 96, and 97.
47643 in base 45 = NNX and consists of only the digits 'N' and 'X'.

The number 47643 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A157443: 121n^2 - 38n + 3.
A188475: (2*n^3 + 3*n^2 + n + 3)/3.
A224257: Number of nX3 0..2 arrays with rows and antidiagonals unimodal and columns nondecreasing

Number of the day: 956122

Johannes Kepler was born on this day 446 years ago.

Johannes Kepler was born on this day 446 years ago.

Jacob Bernoulli was born on this day 363 years ago.

Properties of the number 956122:

956122 = 2 × 193 × 2477 is a sphenic number and squarefree.
956122 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 475392 totatives.
956122 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 956122 results in a prime.
956122 is the difference of 2 positive pentagonal numbers in 4 ways.
956122 = 591² + 779² = 131² + 969² is the sum of 2 positive squares in 2 ways.
956122 = 23² + 168² + 963² is the sum of 3 positive squares.
956122² = 470630² + 832272² = 257560² + 920778² = 253878² + 921800² = 674728² + 677430² is the sum of 2 positive squares in 4 ways.
956122² is the sum of 3 positive squares.
956122 is a proper divisor of 1931⁶¹⁹ - 1.
956122 = '95' + '6122' is the concatenation of 2 semiprime numbers.

Number of the day: 563497217

Charles Hermite was born on this day 195 years ago.

Properties of the number 563497217:

563497217 is a cyclic number.
563497217 = 23 × 24499879 is semiprime and squarefree.
563497217 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 538997316 totatives.
Reversing the decimal digits of 563497217 results in an emirpimes.
563497217 = 281748609² - 281748608² = 12249951² - 12249928² is the difference of 2 nonnegative squares in 2 ways.
563497217 is the difference of 2 positive pentagonal numbers in 2 ways.
563497217 = 34² + 619² + 23730² is the sum of 3 positive squares.
563497217² is the sum of 3 positive squares.
563497217 is a proper divisor of 761¹⁵⁵¹ - 1.
563497217 = '56349721' + '7' is the concatenation of 2 prime numbers.
563497217 is an emirpimes in (at least) the following bases: 2, 5, 6, 10, 12, 13, 17, 19, 21, 23, 29, 33, 37, 39, 40, 48, 49, 50, 51, 57, 60, 61, 64, 65, 66, 67, 70, 83, 84, 89, 91, 94, and 97.

Number of the day: 97548

Properties of the number 97548:

97548 = 2² × 3 × 11 × 739 is the 88168^th composite number and is not squarefree.
97548 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 29520 totatives.
97548 has a semiprime digit sum 33 in base 10.
97548 = 24388² - 24386² = 8132² - 8126² = 2228² - 2206² = 772² - 706² is the difference of 2 nonnegative squares in 4 ways.
97548 is the sum of 2 positive triangular numbers.
97548 is the difference of 2 positive pentagonal numbers in 2 ways.
97548 = 2² + 38² + 310² is the sum of 3 positive squares.
97548² is the sum of 3 positive squares.
97548 is a proper divisor of 419⁶ - 1.
97548 is palindromic in (at least) the following bases: 63, and -55.
97548 in base 54 = XOO and consists of only the digits 'O' and 'X'.

The number 97548 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A047003: T(n,n-1), array T given by A047000.
A149915: 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, 0), (-1, 0, 1), (-1, 1, -1), (0, 0, 1), (1, 0, 0)}
A292346: The forgotten topological index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.1).

Number of the day: 301992

Srinivasa Ramanujan was born on this day 130 years ago.

Properties of the number 301992:

301992 = 2³ × 3 × 12583 is the 275829^th composite number and is not squarefree.
301992 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 100656 totatives.
Reversing the decimal digits of 301992 results in a sphenic number.
301992 = 75499² - 75497² = 37751² - 37747² = 25169² - 25163² = 12589² - 12577² is the difference of 2 nonnegative squares in 4 ways.
301992 = 2² + 112² + 538² is the sum of 3 positive squares.
301992² is the sum of 3 positive squares.
301992 is a proper divisor of 1697⁶ - 1.

Number of the day: 8733

Properties of the number 8733:

8733 is a cyclic number.
8733 = 3 × 41 × 71 is a sphenic number and squarefree.
8733 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 5600 totatives.
8733 has a semiprime digit sum 21 in base 10.
8733 has a Fibonacci digit sum 21 in base 10.
8733 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 8733 results in a sphenic number.
8733 = 4367² - 4366² = 1457² - 1454² = 127² - 86² = 97² - 26² is the difference of 2 nonnegative squares in 4 ways.
8733 is the sum of 2 positive triangular numbers.
8733 is the difference of 2 positive pentagonal numbers in 1 way.
8733 = 10² + 13² + 92² is the sum of 3 positive squares.
8733² = 1917² + 8520² is the sum of 2 positive squares in 1 way.
8733² is the sum of 3 positive squares.
8733 is a proper divisor of 877⁵ - 1.
8733 = '87' + '33' is the concatenation of 2 semiprime numbers.
8733 is palindromic in (at least) the following bases: 23, 43, 74, and -27.
8733 in base 23 = gbg and consists of only the digits 'b' and 'g'.
8733 in base 26 = cnn and consists of only the digits 'c' and 'n'.
8733 in base 42 = 4dd and consists of only the digits '4' and 'd'.
8733 in base 43 = 4V4 and consists of only the digits '4' and 'V'.

The number 8733 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005320: a(n) = 4*a(n-1) - a(n-2), with a(0) = 0, a(1) = 3.
A041016: Numerators of continued fraction convergents to sqrt(12).
A131039: Expansion of (1-x)*(2*x^2-4*x+1)/(1-2*x+5*x^2-4*x^3+x^4).
A143642: Numerators of principal and intermediate convergents to 3^(1/2).
A143643: Lower principal and intermediate convergents to 3^(1/2).
A194480: T(n,k) = number of ways to arrange k indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
A212064: Number of (w,x,y,z) with all terms in {1,...,n} and w^2>=x*y*z.
A227418: Array A(n,k) with all numbers m such that 3*m^2 +- 3^k is a square and their corresponding square roots, read downward by diagonals.
A229362: a(n) = n for n = 1, 2, 3; for n > 3: a(n) = number of partitions of n into preceding terms.
A259593: Numerators of the other-side convergents to sqrt(3).

Number of the day: 2298

Properties of the number 2298:

2298 = 2 × 3 × 383 is a sphenic number and squarefree.
2298 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 764 totatives.
2298 has a semiprime digit sum 21 in base 10.
2298 has a Fibonacci digit sum 21 in base 10.
2298 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 2298 results in a sphenic number.
2298 is the sum of 2 positive triangular numbers.
2298 is the difference of 2 positive pentagonal numbers in 2 ways.
2298 = 5² + 8² + 47² is the sum of 3 positive squares.
2298² is the sum of 3 positive squares.
2298 is a proper divisor of 1531² - 1.
2298 is palindromic in (at least) the following bases: 27, 28, and -41.
2298 in base 3 = 10011010 and consists of only the digits '0' and '1'.
2298 in base 9 = 3133 and consists of only the digits '1' and '3'.
2298 in base 15 = a33 and consists of only the digits '3' and 'a'.
2298 in base 19 = 66i and consists of only the digits '6' and 'i'.
2298 in base 26 = 3aa and consists of only the digits '3' and 'a'.
2298 in base 27 = 343 and consists of only the digits '3' and '4'.
2298 in base 28 = 2q2 and consists of only the digits '2' and 'q'.
2298 in base 47 = 11g and consists of only the digits '1' and 'g'.

The number 2298 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.
A051228: Bernoulli number B_{n} has denominator 42.
A083096: Numbers n such that 3 divides sum(k=1,n, C(2k,k) ).
A084785: Diagonal of the triangle (A084783) and the self-convolution of the first column (A084784).
A090801: List of distinct numbers appearing as denominators of Bernoulli numbers.
A217729: Trajectory of 40 under the map n-> A006369(n).
A218038: Numbers n such that Q(sqrt(n)) has class number 6.
A225196: Number of 6-line partitions of n (i.e., planar partitions of n with at most 6 lines).
A269606: T(n,k)=Number of length-n 0..k arrays with no repeated value differing from the previous repeated value by one or less.
A270850: T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1, k or k-1 exactly once.

Number of the day: 91686001

Properties of the number 91686001:

91686001 is a cyclic number.
91686001 = 11 × 19 × 193 × 2273 is the 86376850^th composite number and is squarefree.
91686001 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 78520320 totatives.
91686001 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 91686001 results in a sphenic number.
91686001 = 45843001² - 45843000² = 4167551² - 4167540² = 2412799² - 2412780² = 237625² - 237432² = 219449² - 219240² = 22655² - 20532² = 21305² - 19032² = 14335² - 10668² is the difference of 2 nonnegative squares in 8 ways.
91686001 is the sum of 2 positive triangular numbers.
91686001 is the difference of 2 positive pentagonal numbers in 8 ways.
91686001 = 369² + 556² + 9552² is the sum of 3 positive squares.
91686001² = 60384280² + 68993199² = 45130415² + 79809576² = 16184751² + 90246200² = 30333424² + 86522865² is the sum of 2 positive squares in 4 ways.
91686001² is the sum of 3 positive squares.
91686001 is a proper divisor of 1493⁹⁶⁰ - 1.
91686001 = '9' + '1686001' is the concatenation of 2 semiprime numbers.

Number of the day: 61348

Marius Sophus Lie was born on this day 175 years ago.

Properties of the number 61348:

61348 = 2² × 7² × 313 is the 55175^th composite number and is not squarefree.
61348 has 3 distinct prime factors, 18 divisors, 15 antidivisors and 26208 totatives.
61348 has a semiprime digit sum 22 in base 10.
61348 = 15338² - 15336² = 2198² - 2184² = 362² - 264² is the difference of 2 nonnegative squares in 3 ways.
61348 is the difference of 2 positive pentagonal numbers in 3 ways.
61348 = 168² + 182² is the sum of 2 positive squares in 1 way.
61348 = 38² + 48² + 240² is the sum of 3 positive squares.
61348² = 4900² + 61152² is the sum of 2 positive squares in 1 way.
61348² is the sum of 3 positive squares.
61348 is a proper divisor of 1877¹⁴ - 1.
61348 is palindromic in (at least) base 5.
61348 in base 3 = 10010011011 and consists of only the digits '0' and '1'.
61348 in base 25 = 3n3n and consists of only the digits '3' and 'n'.
61348 in base 27 = 3344 and consists of only the digits '3' and '4'.
61348 in base 39 = 11D1 and consists of only the digits '1' and 'D'.
61348 in base 45 = UDD and consists of only the digits 'D' and 'U'.

The number 61348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A027105: a(n) =Sum{T(n,k)*T(n,2n-k)}, 0<=k<=n-1, T given by A027082.
A217631: Number of nX2 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nX2 array
A241431: Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4
A276492: Numbers n such that 5*10^n + 59 is prime.

Number of the day: 875875

Properties of the number 875875:

875875 = 5³ × 7² × 11 × 13 is the 806354^th composite number and is not squarefree.
875875 has 4 distinct prime factors, 48 divisors, 59 antidivisors and 504000 totatives.
875875 has sum of divisors equal to 1493856 which is a triangular number.
875875 is the difference of 2 nonnegative squares in 24 ways.
875875 is the difference of 2 positive pentagonal numbers in 21 ways.
875875 = 25² + 69² + 933² is the sum of 3 positive squares.
875875² = 336875² + 808500² = 215600² + 848925² = 444675² + 754600² = 549780² + 681835² = 97020² + 870485² = 30723² + 875336² = 599907² + 638176² = 525525² + 700700² = 245245² + 840840² = 308308² + 819819² is the sum of 2 positive squares in 10 ways.
875875² is the sum of 3 positive squares.
875875 is a proper divisor of 307²⁸ - 1.
875875 = '87587' + '5' is the concatenation of 2 prime numbers.

The number 875875 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A100646: Denominator of Cotesian number C(n,2).
A160555: Denominator of Laguerre(n, -12).
A160608: Denominator of Laguerre(n, -6).
A160632: Denominator of Laguerre(n, 6).
A160672: Denominator of Laguerre(n, 12).
A185505: a(n) = (7*n^4 + 5*n^2)/12.

Number of the day: 4286

János Bolyai was born on this day 215 years ago.

Properties of the number 4286:

4286 = 2 × 2143 is semiprime and squarefree.
4286 has 2 distinct prime factors, 4 divisors, 3 antidivisors and 2142 totatives.
4286 has an oblong digit sum 20 in base 10.
4286 = 5² + 6² + 65² is the sum of 3 positive squares.
4286² is the sum of 3 positive squares.
4286 is a proper divisor of 349³ - 1.
4286 is an emirpimes in (at least) the following bases: 9, 13, 14, 15, 27, 28, 34, 35, 36, 43, 44, 45, 52, 53, 55, 58, 59, 62, 63, 64, 69, 71, 74, 81, 84, 86, 89, 91, and 98.
4286 is palindromic in (at least) the following bases: 19, 23, 42, -51, and -63.
4286 in base 17 = ee2 and consists of only the digits '2' and 'e'.
4286 in base 19 = bgb and consists of only the digits 'b' and 'g'.
4286 in base 22 = 8ii and consists of only the digits '8' and 'i'.
4286 in base 23 = 828 and consists of only the digits '2' and '8'.
4286 in base 41 = 2MM and consists of only the digits '2' and 'M'.
4286 in base 42 = 2I2 and consists of only the digits '2' and 'I'.

The number 4286 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A070143: Numbers n such that [A070080(n), A070081(n), A070082(n)] is an integer triangle with integer area, having relatively prime side lengths.
A070209: Numbers n such that [A070080(n), A070081(n), A070082(n)] is an integer triangle with integer inradius.
A075277: Interprimes (A024675) which are of the form s*prime, s=2.
A100229: Triangle, read by rows, of the coefficients of [x^k] in G100228(x)^n such that the row sums are 4^n-1 for n>0, where G100228(x) is the g.f. of A100228.
A100230: Main diagonal of triangle A100229.
A111570: a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
A196087: Sum of all parts minus the total numbers of parts of all partitions of n.
A248201: Numbers n such that n-1, n and n+1 are all squarefree semiprimes.
A276743: G.f.: Sum_{n>=0} [ Sum_{k>=1} k^n * x^k ]^n.
A285212: Expansion of Product_{k>=0} (1-x^(3*k+2))^(3*k+2).

Number of the day: 748724

Properties of the number 748724:

748724 = 2² × 187181 is the 688580^th composite number and is not squarefree.
748724 has 2 distinct prime factors, 6 divisors, 43 antidivisors and 374360 totatives.
Reversing the decimal digits of 748724 results in a semiprime.
748724 = 187182² - 187180² is the difference of 2 nonnegative squares in 1 way.
748724 is the difference of 2 positive pentagonal numbers in 1 way.
748724 = 550² + 668² is the sum of 2 positive squares in 1 way.
748724 = 28² + 38² + 864² is the sum of 3 positive squares.
748724² = 143724² + 734800² is the sum of 2 positive squares in 1 way.
748724² is the sum of 3 positive squares.
748724 is a proper divisor of 59¹⁹⁶ - 1.

Number of the day: 380653

George Pólya was born on this day 130 years ago.

Properties of the number 380653:

380653 is a cyclic number.
380653 = 7 × 13 × 47 × 89 is the 348304^th composite number and is squarefree.
380653 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 291456 totatives.
380653 has a semiprime digit sum 25 in base 10.
380653 = 190327² - 190326² = 27193² - 27186² = 14647² - 14634² = 4073² - 4026² = 2183² - 2094² = 2137² - 2046² = 743² - 414² = 617² - 6² is the difference of 2 nonnegative squares in 8 ways.
380653 is the difference of 2 positive pentagonal numbers in 6 ways.
380653 = 51² + 104² + 606² is the sum of 3 positive squares.
380653² = 166803² + 342160² = 22372² + 379995² = 251685² + 285572² = 146405² + 351372² is the sum of 2 positive squares in 4 ways.
380653² is the sum of 3 positive squares.
380653 is a proper divisor of 283⁶⁶ - 1.
380653 is palindromic in (at least) base 46.
380653 in base 34 = 9n9n and consists of only the digits '9' and 'n'.
380653 in base 46 = 3ff3 and consists of only the digits '3' and 'f'.

The number 380653 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A287583: Number of set partitions of [n] such that all absolute differences between least elements of consecutive blocks and between consecutive elements within the blocks are not larger than four.

Number of the day: 732499

Properties of the number 732499:

732499 is a cyclic number.
732499 = 31 × 23629 is semiprime and squarefree.
732499 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 708840 totatives.
732499 has a semiprime digit sum 34 in base 10.
732499 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 732499 results in a prime.
732499 = 366250² - 366249² = 11830² - 11799² is the difference of 2 nonnegative squares in 2 ways.
732499 is the difference of 2 positive pentagonal numbers in 2 ways.
732499 = 33² + 103² + 849² is the sum of 3 positive squares.
732499² = 87451² + 727260² is the sum of 2 positive squares in 1 way.
732499² is the sum of 3 positive squares.
732499 is a proper divisor of 1373⁶⁶⁰ - 1.
732499 = '73249' + '9' is the concatenation of 2 semiprime numbers.
732499 is an emirpimes in (at least) the following bases: 3, 4, 7, 8, 13, 16, 17, 22, 28, 29, 33, 35, 38, 39, 41, 49, 50, 58, 60, 62, 63, 66, 67, 68, 69, 73, 74, 77, 79, 80, 82, 83, 89, 90, 91, 96, and 100.
732499 is palindromic in (at least) the following bases: 26, and -92.
732499 in base 5 = 141414444 and consists of only the digits '1' and '4'.

Number of the day: 892849

Properties of the number 892849:

892849 is a cyclic number.
892849 is the 70763^th prime.
892849 has 13 antidivisors and 892848 totatives.
Reversing the decimal digits of 892849 results in a sphenic number.
892849 = 446425² - 446424² is the difference of 2 nonnegative squares in 1 way.
892849 is the sum of 2 positive triangular numbers.
892849 is the difference of 2 positive pentagonal numbers in 1 way.
892849 = 60² + 943² is the sum of 2 positive squares in 1 way.
892849 = 218² + 387² + 834² is the sum of 3 positive squares.
892849² = 113160² + 885649² is the sum of 2 positive squares in 1 way.
892849² is the sum of 3 positive squares.
892849 is a proper divisor of 1741⁹⁷⁹ - 1.
892849 is an emirp in (at least) the following bases: 5, 13, 14, 15, 22, 25, 28, 29, 40, 59, 75, 81, 86, and 99.

Number of the day: 77679

Carl Gustav Jacob Jacobi was born on this day 213 years ago.

Properties of the number 77679:

77679 = 3⁴ × 7 × 137 is the 70046^th composite number and is not squarefree.
77679 has 3 distinct prime factors, 20 divisors, 23 antidivisors and 44064 totatives.
77679 has a triangular digit sum 36 in base 10.
77679 = 6³ + 15³ + 42³ is the sum of 3 positive cubes in 1 way.
77679 is the difference of 2 nonnegative squares in 10 ways.
77679 is the difference of 2 positive pentagonal numbers in 1 way.
77679 is not the sum of 3 positive squares.
77679² = 49896² + 59535² is the sum of 2 positive squares in 1 way.
77679² is the sum of 3 positive squares.
77679 is a proper divisor of 1097¹⁸ - 1.
77679 = '77' + '679' is the concatenation of 2 semiprime numbers.
77679 is palindromic in (at least) the following bases: 47, 90, and -54.
77679 in base 47 = Z7Z and consists of only the digits '7' and 'Z'.
77679 in base 53 = RYY and consists of only the digits 'R' and 'Y'.

The number 77679 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A211545: Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>0.
A274361: Numbers n such that n and n+1 both have 20 divisors.
A293440: First differences of A293230: how many more alive nodes there are in generation n+1 than in generation n in the binary tree of persistently squarefree numbers.

Number of the day: 4815

Properties of the number 4815:

4815 = 3² × 5 × 107 is the 4166^th composite number and is not squarefree.
4815 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 2544 totatives.
4815 = 29² + … + 33² is the sum of at least 2 consecutive positive squares in 1 way.
4815 = 7³ + 12³ + 14³ is the sum of 3 positive cubes in 1 way.
4815 = 2408² - 2407² = 804² - 801² = 484² - 479² = 272² - 263² = 168² - 153² = 76² - 31² is the difference of 2 nonnegative squares in 6 ways.
4815 is the difference of 2 positive pentagonal numbers in 1 way.
4815 is not the sum of 3 positive squares.
4815² = 2889² + 3852² is the sum of 2 positive squares in 1 way.
4815² is the sum of 3 positive squares.
4815 is a proper divisor of 641⁶ - 1.
4815 = '4' + '815' is the concatenation of 2 semiprime numbers.
4815 is palindromic in (at least) the following bases: 6, 58, and -83.
4815 in base 24 = 88f and consists of only the digits '8' and 'f'.
4815 in base 57 = 1RR and consists of only the digits '1' and 'R'.
4815 in base 58 = 1P1 and consists of only the digits '1' and 'P'.

The number 4815 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001522: Number of n-stacks with strictly receding walls, or planar partitions of n.
A027578: Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
A051865: 13-gonal (or tridecagonal) numbers: a(n) = n*(11*n - 9)/2.
A090669: Numbers n such that 7^n - 2 is a prime.
A121035: Multiples of 15 containing a 15 in their decimal representation.
A131246: Row sums of triangle A131245.
A226514: Column 3 of array in A226513.
A238128: Triangle read by rows: T(n,k) gives the number of ballot sequences of length n having largest descent k, n>=0, 0<=k<=n.
A257211: Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit.
A275172: Positions of 3 in A274640.

Number of the day: 429203302

Jacques Salomon Hadamard was born on this day 152 years ago.

Julia Robinson was born on this day 98 years ago.

Properties of the number 429203302:

429203302 = 2 × 11 × 19509241 is a sphenic number and squarefree.
429203302 has 3 distinct prime factors, 8 divisors, 39 antidivisors and 195092400 totatives.
429203302 has a semiprime digit sum 25 in base 10.
429203302 is the sum of 2 positive triangular numbers.
429203302 is the difference of 2 positive pentagonal numbers in 2 ways.
429203302 = 86² + 291² + 20715² is the sum of 3 positive squares.
429203302² = 301444198² + 305527200² is the sum of 2 positive squares in 1 way.
429203302² is the sum of 3 positive squares.
429203302 is a proper divisor of 683¹⁶²⁵⁷⁷ - 1.
429203302 = '429203' + '302' is the concatenation of 2 semiprime numbers.
429203302 = '42' + '9203302' is the concatenation of 2 sphenic numbers.

Number of the day: 696787

Properties of the number 696787:

696787 = 7 × 13² × 19 × 31 is the 640473^th composite number and is not squarefree.
696787 has 4 distinct prime factors, 24 divisors, 47 antidivisors and 505440 totatives.
696787 has a prime digit sum 43 in base 10.
696787 = 83³ + 50³ is the sum of 2 positive cubes in 1 way.
696787 is the difference of 2 nonnegative squares in 12 ways.
696787 is the sum of 2 positive triangular numbers.
696787 is the difference of 2 positive pentagonal numbers in 12 ways.
696787 = 39² + 121² + 825² is the sum of 3 positive squares.
696787² = 267995² + 643188² = 490637² + 494760² is the sum of 2 positive squares in 2 ways.
696787² is the sum of 3 positive squares.
696787 is a proper divisor of 191³ - 1.
696787 = '69' + '6787' is the concatenation of 2 semiprime numbers.

The number 696787 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001872: Convolved Fibonacci numbers.
A061179: Fourth column (m=3) of triangle A060920 (bisection of Fibonacci triangle, even part).
A163763: Sqrt(sigma(A008847(n)^2)), where A008847 lists m such that sigma(m^2) is a square.

Number of the day: 1666

Properties of the number 1666:

1666 = 2 × 7² × 17 is the 1404^th composite number and is not squarefree.
1666 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 672 totatives.
1666 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 1666 results in a prime.
1666 is the difference of 2 positive pentagonal numbers in 4 ways.
1666 = 21² + 35² is the sum of 2 positive squares in 1 way.
1666 = 1² + 24² + 33² is the sum of 3 positive squares.
1666² = 784² + 1470² is the sum of 2 positive squares in 1 way.
1666² is the sum of 3 positive squares.
1666 is a proper divisor of 883² - 1.
1666 = '166' + '6' is the concatenation of 2 semiprime numbers.
1666 = '1' + '666' is the concatenation of 2 triangular numbers.
1666 is palindromic in (at least) the following bases: 26, 37, 48, 97, -32, and -45.
1666 in base 6 = 11414 and consists of only the digits '1' and '4'.
1666 consists of only the digits '1' and '6'.
1666 in base 23 = 33a and consists of only the digits '3' and 'a'.
1666 in base 25 = 2gg and consists of only the digits '2' and 'g'.
1666 in base 26 = 2c2 and consists of only the digits '2' and 'c'.
1666 in base 36 = 1aa and consists of only the digits '1' and 'a'.
1666 in base 37 = 181 and consists of only the digits '1' and '8'.
1666 in base 40 = 11Q and consists of only the digits '1' and 'Q'.

The number 1666 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026798: Number of partitions of n in which the least part is 5.
A033547: Otto Haxel's guess for magic numbers of nuclear shells.
A035607: Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d>=1, m >= 0).
A054252: Triangle T(n,k) of n X n binary matrices with k=0..n^2 ones under action of dihedral group of the square D_4.
A132760: a(n) = n(n+15).
A145540: Number of numbers removed in each step of Eratosthenes' sieve for 10^4.
A185325: Number of partitions of n into parts >= 5.
A191726: Dispersion of A047216, (numbers >1 and congruent to 1 or 2 mod 5), by antidiagonals.
A195313: Generalized 13-gonal numbers: n*(11*n-9)/2, n=0,1,-1,2,-2,...
A292456: Numbers where 6 outnumbers any other digit.

Number of the day: 629435

Properties of the number 629435:

629435 is a cyclic number.
629435 = 5 × 125887 is semiprime and squarefree.
629435 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 503544 totatives.
629435 has a prime digit sum 29 in base 10.
629435 has an oblong digit product 6480 in base 10.
629435 = 314718² - 314717² = 62946² - 62941² is the difference of 2 nonnegative squares in 2 ways.
629435 is the difference of 2 positive pentagonal numbers in 2 ways.
629435 = 15² + 19² + 793² is the sum of 3 positive squares.
629435² = 377661² + 503548² is the sum of 2 positive squares in 1 way.
629435² is the sum of 3 positive squares.
629435 is a proper divisor of 151²⁰⁹⁸¹ - 1.
629435 is an emirpimes in (at least) the following bases: 3, 7, 9, 11, 12, 15, 16, 19, 23, 25, 26, 31, 33, 35, 38, 44, 47, 48, 50, 53, 55, 61, 63, 65, 69, 70, 72, 73, 75, 76, 77, 82, 84, 92, 94, 95, 97, and 98.

Number of the day: 64118

Properties of the number 64118:

64118 = 2 × 32059 is semiprime and squarefree.
64118 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 32058 totatives.
64118 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 64118 results in a sphenic number.
64118 = 3² + 10² + 253² is the sum of 3 positive squares.
64118² is the sum of 3 positive squares.
64118 is a proper divisor of 1901³⁹ - 1.
64118 is an emirpimes in (at least) the following bases: 2, 4, 5, 6, 11, 19, 22, 23, 26, 29, 31, 36, 44, 47, 52, 55, 63, 67, 68, 69, 71, 75, 78, 79, 82, 87, 90, 92, 94, and 97.
64118 is palindromic in (at least) base 49.
64118 in base 49 = QYQ and consists of only the digits 'Q' and 'Y'.

Number of the day: 887818

Properties of the number 887818:

887818 = 2 × 443909 is semiprime and squarefree.
887818 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 443908 totatives.
887818 is the difference of 2 positive pentagonal numbers in 2 ways.
887818 = 533² + 777² is the sum of 2 positive squares in 1 way.
887818 = 88² + 207² + 915² is the sum of 3 positive squares.
887818² = 319640² + 828282² is the sum of 2 positive squares in 1 way.
887818² is the sum of 3 positive squares.
887818 is a proper divisor of 7¹¹⁰⁹⁷⁷ - 1.
887818 is an emirpimes in (at least) the following bases: 8, 13, 14, 15, 17, 19, 21, 25, 27, 32, 34, 40, 41, 46, 50, 52, 54, 56, 58, 61, 62, 75, 81, 84, 86, 88, 92, 93, and 97.

Number of the day: 285694

Nikolai Lobachevsky was born on this day 225 years ago.

Properties of the number 285694:

285694 = 2 × 211 × 677 is a sphenic number and squarefree.
285694 has 3 distinct prime factors, 8 divisors, 51 antidivisors and 141960 totatives.
285694 has a semiprime digit sum 34 in base 10.
285694 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 285694 results in a semiprime.
285694 is the sum of 2 positive triangular numbers.
285694 is the difference of 2 positive pentagonal numbers in 3 ways.
285694 = 22² + 57² + 531² is the sum of 3 positive squares.
285694² = 21944² + 284850² is the sum of 2 positive squares in 1 way.
285694² is the sum of 3 positive squares.
285694 is a proper divisor of 1811⁹¹ - 1.
285694 is palindromic in (at least) the following bases: -7, and -92.
285694 in base 26 = g6g6 and consists of only the digits '6' and 'g'.

The number 285694 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A173674: ceil[A003269(n)/2].