Number of the day: 7928

Properties of the number 7928:

7928 = 2³ × 991 is the 6926^th composite number and is not squarefree.
7928 has 2 distinct prime factors, 8 divisors, 17 antidivisors and 3960 totatives.
7928 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7928 results in a prime.
7928 = 1983² - 1981² = 993² - 989² is the difference of 2 nonnegative squares in 2 ways.
7928 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
7928 = 20² + 38² + 78² is the sum of 3 positive squares.
7928² is the sum of 3 positive squares.
7928 is a proper divisor of 113³ - 1.
7928 is palindromic in (at least) the following bases: 30, 34, and -33.
7928 in base 22 = g88 and consists of only the digits '8' and 'g'.
7928 in base 30 = 8o8 and consists of only the digits '8' and 'o'.
7928 in base 34 = 6t6 and consists of only the digits '6' and 't'.
7928 in base 44 = 448 and consists of only the digits '4' and '8'.

The number 7928 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A072895: Least k for the Theodorus spiral to complete n revolutions.
A107924: Even numbers n such that n^2 is an arithmetic number.
A172213: Number of ways to place 4 nonattacking knights on a 4 X n board.
A199118: Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.
A209990: Number of 2 X 2 matrices having all elements in {-n,...n} and determinant 5.
A258449: Numbers n such that A062234(n) = A062234(n+1) = A062234(n+2).
A318243: Triangle read by rows giving the sum of the number of k-matchings of the graphs obtained by deleting one edge and its two vertices from the ladder graph L_n = P_2 X P_n in all possible ways.
A320647: Triangle read by rows: T(n,k) is the number of chiral pairs of cycles of length n (1) with a color pattern of exactly k colors or equivalently (2) partitioned into k nonempty subsets.
A324802: T(n,k) is the number of non-equivalent distinguishing partitions of the cycle on n vertices with exactly k parts. Regular triangle read by rows, n >= 1, 1 <= k <= n.
A325193: Number of integer partitions whose sum plus co-rank is n, where co-rank is maximum of length and largest part.

Number of the day: 319488687

Carl David Tolmé Runge was born on this day 164 years ago.

Olga Taussky-Todd was born on this day 114 years ago.

Properties of the number 319488687:

319488687 = 3² × 7 × 41 × 179 × 691 is the 302239558^th composite number and is not squarefree.
319488687 has 5 distinct prime factors, 48 divisors, 79 antidivisors and 176860800 totatives.
319488687 is the difference of 2 nonnegative squares in 24 ways.
319488687 is the difference of 2 positive pentagonal numbers in 6 ways.
319488687 is not the sum of 3 positive squares.
319488687² = 70131663² + 311696280² is the sum of 2 positive squares in 1 way.
319488687² is the sum of 3 positive squares.
319488687 is a proper divisor of 359⁶⁹⁰ - 1.
319488687 = '3194' + '88687' is the concatenation of 2 semiprime numbers.

Number of the day: 8653

Properties of the number 8653:

8653 is a cyclic number.
8653 = 17 × 509 is semiprime and squarefree.
8653 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 8128 totatives.
8653 has a semiprime digit sum 22 in base 10.
8653 has sum of divisors equal to 9180 which is a triangular number.
8653 = 4327² - 4326² = 263² - 246² is the difference of 2 nonnegative squares in 2 ways.
8653 is the sum of 2 positive triangular numbers.
8653 is the difference of 2 positive pentagonal numbers in 2 ways.
8653 = 42² + 83² = 2² + 93² is the sum of 2 positive squares in 2 ways.
8653 = 21² + 34² + 84² is the sum of 3 positive squares.
8653² = 5125² + 6972² = 4072² + 7635² = 372² + 8645² = 3740² + 7803² is the sum of 2 positive squares in 4 ways.
8653² is the sum of 3 positive squares.
8653 is a proper divisor of 1019² - 1.
8653 is an emirpimes in (at least) the following bases: 3, 5, 9, 11, 15, 17, 19, 23, 25, 27, 29, 34, 38, 40, 43, 45, 47, 49, 52, 54, 56, 57, 60, 63, 64, 66, 69, 70, 71, 74, 75, 78, 79, 80, 82, 83, 85, 87, 89, 90, 91, 92, 93, 94, 95, and 100.
8653 is palindromic in (at least) the following bases: 33, 50, 84, -29, -35, and -46.
8653 in base 28 = b11 and consists of only the digits '1' and 'b'.
8653 in base 33 = 7v7 and consists of only the digits '7' and 'v'.
8653 in base 46 = 445 and consists of only the digits '4' and '5'.
8653 in base 49 = 3TT and consists of only the digits '3' and 'T'.
8653 in base 50 = 3N3 and consists of only the digits '3' and 'N'.

The number 8653 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022272: a(n) = n*(15*n - 1)/2.
A055004: Boris Stechkin's function.
A096377: Floor of area of triangle with consecutive prime sides.
A158594: Numbers which yield a prime whenever a 3 is prefixed, appended or inserted.
A165584: a(n) = Least i in range [A165583(n),A165583(n+1)] for which abs(A165582(i)) gets the maximum value in that range.
A190816: a(n) = 5*n^2 - 4*n + 1.
A206555: Number of 5's in the last section of the set of partitions of n.
A212083: Beach-Williams Pell numbers of type k^2 + 4.
A214405: Numbers of the form (4k+3)^2-8 or (4k+5)^2+4.
A249993: Expansion of 1/((1+x)*(1+2*x)*(1-4*x)).

Number of the day: 70295

Properties of the number 70295:

70295 is a cyclic number.
70295 = 5 × 17 × 827 is a sphenic number and squarefree.
70295 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 52864 totatives.
70295 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 70295 results in a prime.
70295 = 35148² - 35147² = 7032² - 7027² = 2076² - 2059² = 456² - 371² is the difference of 2 nonnegative squares in 4 ways.
70295 is the difference of 2 positive pentagonal numbers in 4 ways.
70295 is not the sum of 3 positive squares.
70295² = 42177² + 56236² = 29772² + 63679² = 10751² + 69468² = 33080² + 62025² is the sum of 2 positive squares in 4 ways.
70295² is the sum of 3 positive squares.
70295 is a proper divisor of 557²⁸ - 1.
70295 is palindromic in (at least) the following bases: 49, and -70.
70295 in base 49 = TDT and consists of only the digits 'D' and 'T'.

The number 70295 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A254872: Seventh partial sums of sixth powers (A001014).

Number of the day: 33243775211

Giuseppe Peano was born on this day 162 years ago.

Properties of the number 33243775211:

33243775211 is a cyclic number.
33243775211 is prime.
33243775211 has 21 antidivisors and 33243775210 totatives.
33243775211 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 33243775211 results in a semiprime.
33243775211 = 16621887606² - 16621887605² is the difference of 2 nonnegative squares in 1 way.
33243775211 is the difference of 2 positive pentagonal numbers in 1 way.
33243775211 = 439² + 669² + 182327² is the sum of 3 positive squares.
33243775211² is the sum of 3 positive squares.
33243775211 is a proper divisor of 97^55498790 - 1.
33243775211 is an emirp in (at least) the following bases: 16, 35, 47, 61, and 83.

Number of the day: 435635

Properties of the number 435635:

435635 = 5 × 151 × 577 is a sphenic number and squarefree.
435635 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 345600 totatives.
435635 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 435635 results in a semiprime.
435635 = 217818² - 217817² = 43566² - 43561² = 1518² - 1367² = 666² - 89² is the difference of 2 nonnegative squares in 4 ways.
435635 is the difference of 2 positive pentagonal numbers in 3 ways.
435635 = 25² + 27² + 659² is the sum of 3 positive squares.
435635² = 289467² + 325556² = 261381² + 348508² = 231483² + 369044² = 36240² + 434125² is the sum of 2 positive squares in 4 ways.
435635² is the sum of 3 positive squares.
435635 is a proper divisor of 1693³⁶ - 1.
435635 = '4' + '35635' is the concatenation of 2 semiprime numbers.

Number of the day: 52659880

Properties of the number 52659880:

52659880 = 2³ × 5 × 7 × 13 × 17 × 23 × 37 is the 49508943^th composite number and is not squarefree.
52659880 has 7 distinct prime factors, 256 divisors, 65 antidivisors and 14598144 totatives.
52659880 has a prime digit sum 43 in base 10.
52659880 is the difference of 2 nonnegative squares in 64 ways.
52659880 is the difference of 2 positive pentagonal numbers in 27 ways.
52659880 = 510² + 688² + 7206² is the sum of 3 positive squares.
52659880² = 31595928² + 42127904² = 29603392² + 43551144² = 16224936² + 50098048² = 36568896² + 37891672² = 22303008² + 47703656² = 5625984² + 52358488² = 24496472² + 46615296² = 8053864² + 52040352² = 9259432² + 51839424² = 35456064² + 38934952² = 25331096² + 46167072² = 20911968² + 48329624² = 28815136² + 44076648² = 12962432² + 51039576² = 4291616² + 52484712² = 28485408² + 44290456² = 12581184² + 51134888² = 4683168² + 52451224² = 33607784² + 40541088² = 27449856² + 44939608² = 11391072² + 51413096² = 34245344² + 40003992² = 26735016² + 45368512² = 10575768² + 51586976² = 19182184² + 49041888² = 2239832² + 52612224² = 14944664² + 50494752² = 33359200² + 40745880² = 27724200² + 44770880² = 18341120² + 49362600² = 34924120² + 39412800² = 20253800² + 48609120² = 3393880² + 52550400² = 21735000² + 47965120² = 5003880² + 52421600² = 12268200² + 51210880² = 35915880² + 38511200² = 24781120² + 46464600² = 8372000² + 51990120² = 17078880² + 49813400² is the sum of 2 positive squares in 40 ways.
52659880² is the sum of 3 positive squares.
52659880 is a proper divisor of 47¹² - 1.

Number of the day: 95575808602362

Properties of the number 95575808602362:

95575808602362 = 2 × 3 × 11² × 37 × 199 × 241 × 74189 is composite and not squarefree.
95575808602362 has 7 distinct prime factors, 192 divisors, 123 antidivisors and 27921276979200 totatives.
95575808602362 has a sphenic digit sum 66 in base 10.
95575808602362 has a triangular digit sum 66 in base 10.
95575808602362 is the difference of 2 positive pentagonal numbers in 26 ways.
95575808602362 = 3104² + 7111² + 9776285² is the sum of 3 positive squares.
95575808602362² = 62970491817750² + 71898903678888² = 9737935946112² + 95078429696250² = 22186492935750² + 92965018803888² = 30997559546712² + 90409548677910² = 27049067356410² + 91668332291712² = 55786888698288² + 77605143124410² = 39523021863930² + 87021066028512² = 18135501643512² + 93839430785430² = 66028188241488² + 69101472831930² = 47589614241840² + 82885244804538² = 9163593862038² + 95135501982840² = 40047808499160² + 86780805622038² = 55317225539862² + 77940616809000² is the sum of 2 positive squares in 13 ways.
95575808602362² is the sum of 3 positive squares.
95575808602362 is a proper divisor of 1213³⁹²⁷⁶⁰ - 1.
95575808602362 = '9557' + '5808602362' is the concatenation of 2 semiprime numbers.

Number of the day: 866394740

Properties of the number 866394740:

866394740 = 2² × 5 × 2389 × 18133 is the 822016240^th composite number and is not squarefree.
866394740 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 346393728 totatives.
866394740 has a prime digit sum 47 in base 10.
866394740 = 216598686² - 216598684² = 43319742² - 43319732² = 93054² - 88276² = 30078² - 6188² is the difference of 2 nonnegative squares in 4 ways.
866394740 is the difference of 2 positive pentagonal numbers in 4 ways.
866394740 = 15722² + 24884² = 3908² + 29174² = 14378² + 25684² = 10474² + 27508² is the sum of 2 positive squares in 4 ways.
866394740 = 220² + 758² + 29424² is the sum of 3 positive squares.
866394740² = 519836844² + 693115792² = 46021696² + 865171572² = 198067212² + 843450784² = 452940972² + 738569104² = 126495808² + 857110644² = 576237584² + 646985388² = 361426956² + 787407392² = 228023984² + 835849812² = 372032172² + 782452496² = 413069740² + 761586000² = 171845760² + 849181300² = 319090700² + 805494240² = 555920300² + 664524240² is the sum of 2 positive squares in 13 ways.
866394740² is the sum of 3 positive squares.
866394740 is a proper divisor of 1699⁹⁰⁶⁶ - 1.

Number of the day: 65918

Properties of the number 65918:

65918 = 2 × 23 × 1433 is a sphenic number and squarefree.
65918 has 3 distinct prime factors, 8 divisors, 33 antidivisors and 31504 totatives.
65918 has a prime digit sum 29 in base 10.
65918 is the sum of 2 positive triangular numbers.
65918 is the difference of 2 positive pentagonal numbers in 2 ways.
65918 = 1² + 54² + 251² is the sum of 3 positive squares.
65918² = 27232² + 60030² is the sum of 2 positive squares in 1 way.
65918² is the sum of 3 positive squares.
65918 is a proper divisor of 1091⁸⁸ - 1.
65918 is palindromic in (at least) the following bases: 22, and -51.
65918 in base 22 = 6446 and consists of only the digits '4' and '6'.
65918 in base 50 = QII and consists of only the digits 'I' and 'Q'.
65918 in base 60 = IIc and consists of only the digits 'I' and 'c'.

The number 65918 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A094552: Numbers n such that there are integers a < b with a^2+(a+1)^2+...+(n-1)^2 = (n+1)^2+(n+2)^2+...+b^2.
A159230: 1/8 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 31
A261204: Number of binary strings of length n that avoid the pattern x x^R x (x^R is the reversal of x).

Number of the day: 15625

Augustin-Louis Cauchy was born on this day 231 years ago.

Properties of the number 15625:

15625 = 5⁶ is a prime power and not squarefree.
15625 has 1 distinct prime factor, 7 divisors, 12 antidivisors and 12500 totatives.
15625 has a prime digit sum 19 in base 10.
15625 has a triangular digit product 300 in base 10.
15625 has sum of divisors equal to 19531 which is an emirp.
Reversing the decimal digits of 15625 results in a semiprime.
15625 = 125² is a perfect square.
15625 = 4³ + 17³ + 22³ is the sum of 3 positive cubes in 1 way.
15625 = (124 × 125)/2 + (125 × 126)/2 is the sum of at least 2 consecutive triangular numbers in 1 way. In fact, it is the sum of 2 triangular numbers.
15625 = 7813² - 7812² = 1565² - 1560² = 325² - 300² = 125² - 0² is the difference of 2 nonnegative squares in 4 ways.
15625 is the difference of 2 positive pentagonal numbers in 3 ways.
15625 = 75² + 100² = 35² + 120² = 44² + 117² is the sum of 2 positive squares in 3 ways.
15625 is the sum of 3 positive squares.
15625² = 9375² + 12500² = 4375² + 15000² = 5500² + 14625² = 8400² + 13175² = 1185² + 15580² = 10296² + 11753² is the sum of 2 positive squares in 6 ways.
15625² is the sum of 3 positive squares.
15625 is a proper divisor of 1249⁵⁰ - 1.
15625 is palindromic in (at least) the following bases: 24, 37, 55, 93, and -73.
15625 in base 5 = 1000000 and consists of only the digits '0' and '1'.
15625 in base 24 = 1331 and consists of only the digits '1' and '3'.
15625 in base 25 = 1000 and consists of only the digits '0' and '1'.
15625 in base 37 = BFB and consists of only the digits 'B' and 'F'.
15625 in base 39 = AAP and consists of only the digits 'A' and 'P'.
15625 in base 54 = 5JJ and consists of only the digits '5' and 'J'.
15625 in base 55 = 595 and consists of only the digits '5' and '9'.
15625 in base 62 = 441 and consists of only the digits '1' and '4'.

The number 15625 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000351: Powers of 5: a(n) = 5^n.
A000578: The cubes: a(n) = n^3.
A001014: Sixth powers: a(n) = n^6.
A003593: Numbers of the form 3^i*5^j with i, j >= 0.
A007778: a(n) = n^(n+1).
A023194: Numbers n such that sigma(n) (sum of divisors of n) is prime.
A030516: Numbers with 7 divisors. 6th powers of primes.
A133500: The powertrain or power train map: Powertrain(n): if abcd... is the decimal expansion of a number n, then the powertrain of n is the number n' = a^b*c^d* ..., which ends in an exponent or a base according as the number of digits is even or odd. a(0) = 0 by convention.
A191702: Dispersion of A008587 (5,10,15,20,25,30,...), by antidiagonals.
A241909: Self-inverse permutation of natural numbers: a(1)=1, a(p_i) = 2^i, and if n = p_i1 * p_i2 * p_i3 * ... * p_{ik-1} * p_ik, where p's are primes, with their indexes are sorted into nondescending order: i1 <= i2 <= i3 <= ... <= i_{k-1} <= ik, then a(n) = 2^(i1-1) * 3^(i2-i1) * 5^(i3-i2) * ... * p_k^(1+(ik-i_{k-1})). Here k = A001222(n) and ik = A061395(n).

Number of the day: 465837

Properties of the number 465837:

465837 = 3 × 31 × 5009 is a sphenic number and squarefree.
465837 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 300480 totatives.
465837 has a semiprime digit sum 33 in base 10.
465837 = 232919² - 232918² = 77641² - 77638² = 7529² - 7498² = 2551² - 2458² is the difference of 2 nonnegative squares in 4 ways.
465837 is the difference of 2 positive pentagonal numbers in 2 ways.
465837 = 5² + 94² + 676² is the sum of 3 positive squares.
465837² = 320013² + 338520² is the sum of 2 positive squares in 1 way.
465837² is the sum of 3 positive squares.
465837 is a proper divisor of 463⁸⁰ - 1.
465837 = '46' + '5837' is the concatenation of 2 semiprime numbers.
465837 is palindromic in (at least) base -95.

Number of the day: 61490

Properties of the number 61490:

61490 = 2 × 5 × 11 × 13 × 43 is the 55304^th composite number and is squarefree.
61490 has 5 distinct prime factors, 32 divisors, 19 antidivisors and 20160 totatives.
61490 has an oblong digit sum 20 in base 10.
61490 = 66² + … + 77² is the sum of at least 2 consecutive positive squares in 1 way.
61490 is the sum of 2 positive triangular numbers.
61490 is the difference of 2 positive pentagonal numbers in 6 ways.
61490 = 29² + 40² + 243² is the sum of 3 positive squares.
61490² = 36894² + 49192² = 15136² + 59598² = 31218² + 52976² = 23650² + 56760² is the sum of 2 positive squares in 4 ways.
61490² is the sum of 3 positive squares.
61490 is a proper divisor of 859² - 1.

The number 61490 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008957: Triangle of central factorial numbers T(2*n,2*n-2*k), k >= 0, n >= 1 (in Riordan's notation).
A028269: Distinct even elements in 3-Pascal triangle A028262 (by row).
A028270: Central elements in 3-Pascal triangle A028262 (by row).
A029617: Table read by rows: list of even numbers to the right of the central elements of the (2,3)-Pascal triangle A029600.
A029631: Even numbers to left of central elements of the (3,2)-Pascal triangle A029618.
A036969: Triangle read by rows: T(n,k) = T(n-1,k-1) + k^2*T(n-1,k), 1 < k <= n, T(n,1) = 1.
A081497: Duplicate of A028270.
A192754: Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
A255180: Number of partitions of n in which two summands (of each size) are designated.
A269945: Triangle read by rows, Stirling set numbers of order 2, T(n,n) = 1, T(n,k) = 0 if k<0 or k>n, otherwise T(n,k) = T(n-1,k-1)+k^2*T(n-1, k), for n>=0 and 0<=k<=n.

Number of the day: 781155

Properties of the number 781155:

781155 = 3² × 5 × 17359 is the 718603^th composite number and is not squarefree.
781155 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 416592 totatives.
781155 = 390578² - 390577² = 130194² - 130191² = 78118² - 78113² = 43402² - 43393² = 26046² - 26031² = 8702² - 8657² is the difference of 2 nonnegative squares in 6 ways.
781155 is the sum of 2 positive triangular numbers.
781155 is the difference of 2 positive pentagonal numbers in 2 ways.
781155 = 25² + 29² + 883² is the sum of 3 positive squares.
781155² = 468693² + 624924² is the sum of 2 positive squares in 1 way.
781155² is the sum of 3 positive squares.
781155 is a proper divisor of 131⁶⁶ - 1.
781155 = '781' + '155' is the concatenation of 2 emirpimes.

Number of the day: 653109

Pierre de Fermat was maybe born on this day 419 years ago.

Recent studies have pinpointed his birthday to be around November 1607.

Properties of the number 653109:

653109 = 3 × 29 × 7507 is a sphenic number and squarefree.
653109 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 420336 totatives.
653109 = 326555² - 326554² = 108853² - 108850² = 11275² - 11246² = 3797² - 3710² is the difference of 2 nonnegative squares in 4 ways.
653109 is the sum of 2 positive triangular numbers.
653109 is the difference of 2 positive pentagonal numbers in 2 ways.
653109 = 50² + 103² + 800² is the sum of 3 positive squares.
653109² = 450420² + 472941² is the sum of 2 positive squares in 1 way.
653109² is the sum of 3 positive squares.
653109 is a proper divisor of 607⁸⁴ - 1.
653109 = '653' + '109' is the concatenation of 2 prime numbers.

Number of the day: 5195

Arthur Cayley was born on this day 199 years ago.

Properties of the number 5195:

5195 is a cyclic number.
5195 = 5 × 1039 is semiprime and squarefree.
5195 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 4152 totatives.
5195 has an oblong digit sum 20 in base 10.
5195 = 2598² - 2597² = 522² - 517² is the difference of 2 nonnegative squares in 2 ways.
5195 is the sum of 2 positive triangular numbers.
5195 is the difference of 2 positive pentagonal numbers in 2 ways.
5195 = 9² + 25² + 67² is the sum of 3 positive squares.
5195² = 3117² + 4156² is the sum of 2 positive squares in 1 way.
5195² is the sum of 3 positive squares.
5195 is a proper divisor of 271¹⁷³ - 1.
5195 = '51' + '95' is the concatenation of 2 semiprime numbers.
5195 is an emirpimes in (at least) the following bases: 8, 9, 11, 12, 13, 14, 15, 19, 22, 25, 28, 32, 35, 40, 51, 54, 55, 58, 60, 62, 63, 65, 68, 70, 75, 77, 81, 88, 89, 91, 93, and 99.
5195 is palindromic in (at least) the following bases: 30, 53, -44, and -98.
5195 in base 30 = 5n5 and consists of only the digits '5' and 'n'.
5195 in base 41 = 33T and consists of only the digits '3' and 'T'.
5195 in base 52 = 1ll and consists of only the digits '1' and 'l'.
5195 in base 53 = 1j1 and consists of only the digits '1' and 'j'.

The number 5195 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067989: Row sums of triangle A067979; also of triangle A067990.
A088943: a(n)=60*sum(1<=i<=j<=k<=n,i*j^2/k).
A112068: Positive integers i for which A112049(i) == 8.
A124209: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^61 + n^63 is prime.
A183564: Number of partitions of n containing a clique of size 7.
A238708: Number of strict partitions of n that include a pair of consecutive integers.
A241078: T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order
A246211: Self-inverse permutation of natural numbers: a(0) = 0, a(1) = 1, and for n > 1, if A117966(n) < 0, a(n) = A117967(1+a(-(A117966(n)))), otherwise a(n) = A117968(a(A117966(n)-1)).
A279700: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood.
A294587: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j*x^j)^(j^k).

Number of the day: 56904

Properties of the number 56904:

56904 = 2³ × 3 × 2371 is the 51134^th composite number and is not squarefree.
56904 has 3 distinct prime factors, 16 divisors, 5 antidivisors and 18960 totatives.
Reversing the decimal digits of 56904 results in a sphenic number.
56904 = 14227² - 14225² = 7115² - 7111² = 4745² - 4739² = 2377² - 2365² is the difference of 2 nonnegative squares in 4 ways.
56904 is the sum of 2 positive triangular numbers.
56904 = 58² + 88² + 214² is the sum of 3 positive squares.
56904² is the sum of 3 positive squares.
56904 is a proper divisor of 1907⁶ - 1.
56904 is palindromic in (at least) the following bases: 48, -57, and -63.
56904 in base 48 = OXO and consists of only the digits 'O' and 'X'.
56904 in base 56 = I88 and consists of only the digits '8' and 'I'.

The number 56904 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A119307: Number triangle T(n,k)=sum{k=0..n, C(j,k)C(j,n-k)}.
A222704: Total number of parts of multiplicity 4 in all partitions of n.

Number of the day: 470311082333

Properties of the number 470311082333:

470311082333 is a cyclic number.
470311082333 = 43 × 149 × 1109 × 66191 is composite and squarefree.
470311082333 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 455872240320 totatives.
470311082333 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 470311082333 results in a semiprime.
470311082333 = 235155541167² - 235155541166² = 5468733537² - 5468733494² = 1578225183² - 1578225034² = 212043423² - 212042314² = 36706113² - 36699706² = 4955073² - 4907386² = 3585777² - 3519586² = 1505727² - 1340486² is the difference of 2 nonnegative squares in 8 ways.
470311082333 is the difference of 2 positive pentagonal numbers in 8 ways.
470311082333 = 315² + 562² + 685792² is the sum of 3 positive squares.
470311082333² = 160978961067² + 441903030380² = 103488304680² + 458783919683² = 215856793920² + 417849684317² = 59796088917² + 466494310700² is the sum of 2 positive squares in 4 ways.
470311082333² is the sum of 3 positive squares.
470311082333 is a proper divisor of 1489^25668482 - 1.
470311082333 = '47031108233' + '3' is the concatenation of 2 prime numbers.
470311082333 = '4703110823' + '33' is the concatenation of 2 semiprime numbers.

Number of the day: 7828

Properties of the number 7828:

7828 is the 1892^th totient number.
7828 = 2² × 19 × 103 is the 6838^th composite number and is not squarefree.
7828 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 3672 totatives.
7828 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 7828 results in a prime.
7828 = 1958² - 1956² = 122² - 84² is the difference of 2 nonnegative squares in 2 ways.
7828 is the sum of 2 positive triangular numbers.
7828 is the difference of 2 positive pentagonal numbers in 2 ways.
7828 = 14² + 24² + 84² is the sum of 3 positive squares.
7828² is the sum of 3 positive squares.
7828 is a proper divisor of 571⁶ - 1.
7828 = '78' + '28' is the concatenation of 2 triangular numbers.
7828 is palindromic in (at least) the following bases: 33, -48, and -86.
7828 in base 12 = 4644 and consists of only the digits '4' and '6'.
7828 in base 32 = 7kk and consists of only the digits '7' and 'k'.
7828 in base 33 = 767 and consists of only the digits '6' and '7'.
7828 in base 39 = 55S and consists of only the digits '5' and 'S'.
7828 in base 62 = 22G and consists of only the digits '2' and 'G'.

The number 7828 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A064914: Number of ordered biquanimous partitions of 2n.
A076066: Sums of members of groups in A076063.
A100182: Structured tetragonal anti-prism numbers.
A132432: Number of different values of i^2+j^2+k^2+l^2+m^2 for i,j,k,l,m in [0,n].
A172449: Number of ways to place 8 nonattacking queens on an 8 X n board.
A225414: Ordered counts of internal lattice points within primitive Pythagorean triangles (PPT).
A271454: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 371", based on the 5-celled von Neumann neighborhood.
A273161: a(n) = Sum_{k=1..n} C(n-k, floor((n-k)/k)).
A283213: Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 595", based on the 5-celled von Neumann neighborhood.
A319284: The profiles of the backtrack tree for the n queens problem, triangle read by rows.

Number of the day: 402484

Properties of the number 402484:

402484 = 2² × 100621 is the 368446^th composite number and is not squarefree.
402484 has 2 distinct prime factors, 6 divisors, 25 antidivisors and 201240 totatives.
402484 has a semiprime digit sum 22 in base 10.
402484 has sum of divisors equal to 704354 which is a sphenic number.
402484 = 100622² - 100620² is the difference of 2 nonnegative squares in 1 way.
402484 is the difference of 2 positive pentagonal numbers in 1 way.
402484 = 90² + 628² is the sum of 2 positive squares in 1 way.
402484 = 72² + 362² + 516² is the sum of 3 positive squares.
402484² = 113040² + 386284² is the sum of 2 positive squares in 1 way.
402484² is the sum of 3 positive squares.
402484 is a proper divisor of 733¹² - 1.

Number of the day: 4995

Properties of the number 4995:

4995 = 3³ × 5 × 37 is the 4326^th composite number and is not squarefree.
4995 has 3 distinct prime factors, 16 divisors, 19 antidivisors and 2592 totatives.
4995 has sum of divisors equal to 9120 which is an oblong number.
4995 = 2498² - 2497² = 834² - 831² = 502² - 497² = 282² - 273² = 174² - 159² = 106² - 79² = 86² - 49² = 78² - 33² is the difference of 2 nonnegative squares in 8 ways.
4995 is the sum of 2 positive triangular numbers.
4995 is the difference of 2 positive pentagonal numbers in 1 way.
4995 = 17² + 35² + 59² is the sum of 3 positive squares.
4995² = 2997² + 3996² = 2808² + 4131² = 1539² + 4752² = 1620² + 4725² is the sum of 2 positive squares in 4 ways.
4995² is the sum of 3 positive squares.
4995 is a proper divisor of 487⁴ - 1.
4995 = '499' + '5' is the concatenation of 2 prime numbers.
4995 = '4' + '995' is the concatenation of 2 semiprime numbers.
4995 is palindromic in (at least) the following bases: 39, -11, and -48.
4995 in base 38 = 3HH and consists of only the digits '3' and 'H'.
4995 in base 39 = 3B3 and consists of only the digits '3' and 'B'.

The number 4995 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000243: Number of trees with n nodes, 2 of which are labeled.
A000566: Heptagonal numbers (or 7-gonal numbers): n*(5*n-3)/2.
A033571: a(n) = (2*n + 1)*(5*n + 1).
A069534: Smallest multiple of 5 with digit sum n.
A223282: T(n,k)=Rolling icosahedron face footprints: number of nXk 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge
A225513: -9-Kndel numbers.
A226929: Values of n such that L(9) and N(9) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.
A254963: a(n) = n*(11*n + 3)/2.
A282613: Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations.
A324756: Number of integer partitions of n containing no prime indices of the parts.

Number of the day: 509763304

Properties of the number 509763304:

509763304 = 2³ × 59 × 1080007 is the 482920762^th composite number and is not squarefree.
509763304 has 3 distinct prime factors, 16 divisors, 19 antidivisors and 250561392 totatives.
509763304 has an emirp digit sum 37 in base 10.
509763304 = 228³ + 300³ + 778³ is the sum of 3 positive cubes in 1 way.
509763304 = 127440827² - 127440825² = 63720415² - 63720411² = 2160073² - 2159955² = 1080125² - 1079889² is the difference of 2 nonnegative squares in 4 ways.
509763304 is the difference of 2 positive pentagonal numbers in 2 ways.
509763304 = 352² + 978² + 22554² is the sum of 3 positive squares.
509763304² is the sum of 3 positive squares.
509763304 is a proper divisor of 353³⁶⁰⁰⁰² - 1.

Number of the day: 64555

Properties of the number 64555:

64555 = 5 × 12911 is semiprime and squarefree.
64555 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 51640 totatives.
64555 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 64555 results in an emirpimes.
64555 = 32278² - 32277² = 6458² - 6453² is the difference of 2 nonnegative squares in 2 ways.
64555 is the difference of 2 positive pentagonal numbers in 2 ways.
64555 = 23² + 45² + 249² is the sum of 3 positive squares.
64555² = 38733² + 51644² is the sum of 2 positive squares in 1 way.
64555² is the sum of 3 positive squares.
64555 is a proper divisor of 431¹²⁹¹ - 1.
64555 = '6' + '4555' is the concatenation of 2 semiprime numbers.
64555 is an emirpimes in (at least) the following bases: 2, 5, 7, 10, 13, 18, 19, 26, 27, 28, 32, 39, 45, 53, 57, 60, 62, 68, 71, 74, 76, 77, 82, 85, 90, 92, 96, and 97.
64555 is palindromic in (at least) the following bases: 52, 61, and -99.
64555 in base 52 = NjN and consists of only the digits 'N' and 'j'.
64555 in base 60 = Htt and consists of only the digits 'H' and 't'.
64555 in base 61 = HLH and consists of only the digits 'H' and 'L'.

The number 64555 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A113898: Numbers n such that the value pi(n), the number of primes <= n, can be obtained deleting some of the repeating adjacent digits of n.

Number of the day: 6134

Properties of the number 6134:

6134 = 2 × 3067 is semiprime and squarefree.
6134 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 3066 totatives.
6134 has a semiprime digit sum 14 in base 10.
6134 has an oblong digit product 72 in base 10.
6134 = 5² + 22² + 75² is the sum of 3 positive squares.
6134² is the sum of 3 positive squares.
6134 is a proper divisor of 823⁷ - 1.
6134 = '6' + '134' is the concatenation of 2 semiprime numbers.
6134 is an emirpimes in (at least) the following bases: 4, 7, 8, 9, 16, 18, 21, 24, 26, 28, 29, 31, 39, 40, 49, 50, 52, 55, 56, 68, 74, 78, 79, 85, 86, 87, 94, and 99.
6134 is palindromic in (at least) the following bases: 19, 25, and -73.
6134 in base 6 = 44222 and consists of only the digits '2' and '4'.
6134 in base 19 = gig and consists of only the digits 'g' and 'i'.
6134 in base 25 = 9k9 and consists of only the digits '9' and 'k'.

The number 6134 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058787: Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n faces and k vertices, where (n/2+2) <= k <= (2n+8).
A058788: Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n edges and k vertices (or k faces), where (n/3+2) <= k <= (2n/3). Note that there is no such k when n=7.
A100363: Numbers n such that the numbers of divisors of n,n+1 and n+2 are k,2k,4k respectively for some k.
A122370: Dimension of 6-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 6 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( xi w ) = w and d_{xi} ( xj w ) = 0 for i/=j).
A167121: a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.
A173724: Number of reduced, normalized 3x3 semimagic squares with distinct nonnegative integer entries and maximum entry n.
A212438: Irregular triangle read by rows: T(n,k) (n >= 4, k=4..2n-4) = number of polyhedra with n faces and k vertices.
A240733: Floor(6^n/(2+2*cos(Pi/9))^n).
A317222: T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
A318683: Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums.

Number of the day: 208438

Properties of the number 208438:

208438 = 2 × 89 × 1171 is a sphenic number and squarefree.
208438 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 102960 totatives.
208438 has a semiprime digit sum 25 in base 10.
208438 = 11³ + 12³ + 59³ is the sum of 3 positive cubes in 1 way.
208438 is the difference of 2 positive pentagonal numbers in 2 ways.
208438 = 27² + 50² + 453² is the sum of 3 positive squares.
208438² = 91338² + 187360² is the sum of 2 positive squares in 1 way.
208438² is the sum of 3 positive squares.
208438 is a proper divisor of 751⁶⁶ - 1.
208438 is palindromic in (at least) the following bases: 96, -14, -60, and -93.
208438 in base 61 = u11 and consists of only the digits '1' and 'u'.

Number of the day: 665250

William Rowan Hamilton was born on this day 215 years ago.

John Venn was born on this day 186 years ago.

Properties of the number 665250:

665250 = 2 × 3 × 5³ × 887 is the 611280^th composite number and is not squarefree.
665250 has 4 distinct prime factors, 32 divisors, 15 antidivisors and 177200 totatives.
665250 is the difference of 2 positive pentagonal numbers in 3 ways.
665250 = 40² + 77² + 811² is the sum of 3 positive squares.
665250² = 399150² + 532200² = 186270² + 638640² = 234168² + 622674² is the sum of 2 positive squares in 3 ways.
665250² is the sum of 3 positive squares.
665250 is a proper divisor of 751⁴⁴³ - 1.
665250 is palindromic in (at least) base 8.

Number of the day: 71735

Properties of the number 71735:

71735 is a cyclic number.
71735 = 5 × 14347 is semiprime and squarefree.
71735 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 57384 totatives.
71735 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 71735 results in a prime.
71735 = 35868² - 35867² = 7176² - 7171² is the difference of 2 nonnegative squares in 2 ways.
71735 is the difference of 2 positive pentagonal numbers in 2 ways.
71735 is not the sum of 3 positive squares.
71735² = 43041² + 57388² is the sum of 2 positive squares in 1 way.
71735² is the sum of 3 positive squares.
71735 is a proper divisor of 191⁷⁹⁷ - 1.
71735 = '717' + '35' is the concatenation of 2 semiprime numbers.
71735 is an emirpimes in (at least) the following bases: 2, 3, 6, 9, 14, 16, 17, 25, 27, 28, 29, 33, 35, 40, 42, 45, 48, 58, 59, 60, 61, 73, 77, 79, 80, 82, 85, 87, 88, 90, and 93.
71735 is palindromic in (at least) the following bases: 11, -42, -52, and -53.
71735 in base 11 = 49994 and consists of only the digits '4' and '9'.
71735 in base 51 = RTT and consists of only the digits 'R' and 'T'.
71735 in base 52 = QRR and consists of only the digits 'Q' and 'R'.

The number 71735 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A280038: Numerators of fractions converging to limiting value of shifted Fekete polynomials.

Number of the day: 158293

Properties of the number 158293:

158293 is a cyclic number.
158293 is the 14543^th prime.
158293 has 5 antidivisors and 158292 totatives.
158293 has a triangular digit sum 28 in base 10.
158293 has sum of divisors equal to 158294 which is an emirpimes.
Reversing the decimal digits of 158293 results in an emirp.
158293 = 79147² - 79146² is the difference of 2 nonnegative squares in 1 way.
158293 is the sum of 2 positive triangular numbers.
158293 is the difference of 2 positive pentagonal numbers in 1 way.
158293 = 62² + 393² is the sum of 2 positive squares in 1 way.
158293 = 54² + 89² + 384² is the sum of 3 positive squares.
158293² = 48732² + 150605² is the sum of 2 positive squares in 1 way.
158293² is the sum of 3 positive squares.
158293 is a proper divisor of 397⁴³⁹⁷ - 1.
158293 is an emirp in (at least) the following bases: 5, 9, 10, 20, 21, 27, 31, 44, 46, 50, 59, 62, 76, 77, 79, 82, 83, 85, 91, 95, and 96.
158293 is palindromic in (at least) base 73.
158293 in base 4 = 212221111 and consists of only the digits '1' and '2'.

The number 158293 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A226986: Primes p such that both prevprime(p^2) - 2 and nextprime(p^2) + 2 are also primes.
A267821: Primes whose base-9 representation is a square in base 10.
A298693: G.f. A(x) satisfies: A(x) = Sum_{n>=0} binomial( n*(n+1), n)/(n+1) * x^n / A(x)^( n*(n+1) ).

Number of the day: 28203

Properties of the number 28203:

28203 = 3 × 7 × 17 × 79 is the 25128^th composite number and is squarefree.
28203 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 14976 totatives.
28203 has an emirpimes digit sum 15 in base 10.
28203 has a triangular digit sum 15 in base 10.
28203 = 14102² - 14101² = 4702² - 4699² = 2018² - 2011² = 838² - 821² = 682² - 661² = 302² - 251² = 218² - 139² = 178² - 59² is the difference of 2 nonnegative squares in 8 ways.
28203 = (237 × 238)/2 is a triangular number.
28203 is the difference of 2 positive pentagonal numbers in 3 ways.
28203 = 5² + 17² + 167² is the sum of 3 positive squares.
28203² = 13272² + 24885² is the sum of 2 positive squares in 1 way.
28203² is the sum of 3 positive squares.
28203 is a proper divisor of 103⁶ - 1.
28203 is palindromic in (at least) the following bases: 20, 94, and -100.
28203 in base 20 = 3aa3 and consists of only the digits '3' and 'a'.

The number 28203 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A068130: Triangular numbers with sum of digits = 15.
A069702: Triangular numbers with internal digits also forming a triangular number.
A117062: Hexagonal numbers for which the sum of the digits is also a hexagonal number.
A117345: Indices n such that the 3 X 3 matrix with components (row by row) prime(n+k), 0 <= k <= 8, has zero determinant.
A145678: a(n) = 441*n^2 - 21.
A157948: a(n) = 64*n^2 - n.
A212240: Number of 2 X 2 matrices M of with all terms in {1,...,n} and permanent(M) >= n.
A247016: Triangular numbers A000217 composed of only curved digits {0, 2, 3, 5, 6, 8, 9}.
A302428: Number of 3Xn 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A333771: Triangular numbers that are the product of four distinct primes.