Number of the day: 22070

Properties of the number 22070:

22070 = 2 × 5 × 2207 is a sphenic number and squarefree.
22070 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 8824 totatives.
22070 has a prime digit sum 11 in base 10.
22070 is the sum of 2 positive triangular numbers.
22070 is the difference of 2 positive pentagonal numbers in 2 ways.
22070 = 10² + 19² + 147² is the sum of 3 positive squares.
22070² = 13242² + 17656² is the sum of 2 positive squares in 1 way.
22070² is the sum of 3 positive squares.
22070 is a proper divisor of 11¹¹⁰³ - 1.
22070 = '2' + '2070' is the concatenation of 2 oblong numbers.
22070 is palindromic in (at least) the following bases: 43, and -32.
22070 in base 31 = mtt and consists of only the digits 'm' and 't'.
22070 in base 43 = BeB and consists of only the digits 'B' and 'e'.
22070 in base 49 = 99K and consists of only the digits '9' and 'K'.
22070 in base 52 = 88M and consists of only the digits '8' and 'M'.

The number 22070 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004951: Nearest integer to n*phi^16, where phi is the golden ratio, A001622.
A004971: a(n) = ceiling(n*phi^16), where phi is the golden ratio, A001622.
A203552: a(n) = n*(5*n^2 - 3*n + 4) / 6.
A210750: Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section.
A227824: G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(1-x)^(n-k).
A303479: Total volume of the family of rectangular prisms with dimensions p, q, and |q - p| where p divides q, n = p + q and p < q.

Number of the day: 664269

Properties of the number 664269:

664269 = 3 × 179 × 1237 is a sphenic number and squarefree.
664269 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 440016 totatives.
664269 has a semiprime digit sum 33 in base 10.
664269 = 332135² - 332134² = 110713² - 110710² = 1945² - 1766² = 887² - 350² is the difference of 2 nonnegative squares in 4 ways.
664269 is the sum of 2 positive triangular numbers.
664269 is the difference of 2 positive pentagonal numbers in 2 ways.
664269 = 83² + 88² + 806² is the sum of 3 positive squares.
664269² = 328644² + 577275² is the sum of 2 positive squares in 1 way.
664269² is the sum of 3 positive squares.
664269 is a proper divisor of 359²⁰⁶ - 1.

Number of the day: 2033

Properties of the number 2033:

2033 is a cyclic number.
2033 = 19 × 107 is semiprime and squarefree.
2033 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 1908 totatives.
2033 has a Fibonacci digit sum 8 in base 10.
Reversing the decimal digits of 2033 results in a sphenic number.
2033 = 1017² - 1016² = 63² - 44² is the difference of 2 nonnegative squares in 2 ways.
2033 is the difference of 2 positive pentagonal numbers in 1 way.
2033 = 4² + 9² + 44² is the sum of 3 positive squares.
2033² is the sum of 3 positive squares.
2033 is a proper divisor of 643⁹ - 1.
2033 is an emirpimes in (at least) the following bases: 3, 6, 8, 12, 23, 24, 26, 27, 36, 38, 41, 43, 44, 45, 46, 51, 52, 54, 55, 57, 58, 61, 71, 73, 76, 77, 79, 82, 83, 87, 88, 89, 94, and 99.
2033 is palindromic in (at least) the following bases: 5, and -29.
2033 in base 5 = 31113 and consists of only the digits '1' and '3'.
2033 in base 22 = 449 and consists of only the digits '4' and '9'.

The number 2033 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000107: Number of rooted trees with n nodes and a single labeled node; pointed rooted trees; vertebrates.
A037015: Numbers n with property that, reading binary expansion of n from right to left, run lengths strictly increase.
A037308: Numbers k such that (sum of base-2 digits of k) = (sum of base 10 digits of k).
A046865: Numbers k such that 4*5^k - 1 is prime.
A050969: Discriminants of real quadratic fields with class number 1 and related continued fraction period length of 20.
A055103: Expansion of 4th power of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).
A081464: Fractional part of (3/2)^n decreases monotonically to zero.
A107479: a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
A183559: Number of partitions of n containing a clique of size 2.
A198185: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,0,0 for x=0,1,2,3,4

Number of the day: 4977

Properties of the number 4977:

4977 = 3² × 7 × 79 is the 4310^th composite number and is not squarefree.
4977 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 2808 totatives.
4977 = 17³ + 4³ is the sum of 2 positive cubes in 1 way.
4977 = 25³ - 22³ is the difference of 2 positive cubes in 1 way.
4977 = 2489² - 2488² = 831² - 828² = 359² - 352² = 281² - 272² = 129² - 108² = 71² - 8² is the difference of 2 nonnegative squares in 6 ways.
4977 is the difference of 2 positive pentagonal numbers in 1 way.
4977 = 8² + 17² + 68² is the sum of 3 positive squares.
4977² is the sum of 3 positive squares.
4977 is a proper divisor of 631² - 1.
4977 = '49' + '77' is the concatenation of 2 semiprime numbers.
4977 is palindromic in (at least) the following bases: 4, 23, 78, and -24.
4977 in base 23 = 999 and consists of only the digit '9'.
4977 in base 31 = 55h and consists of only the digits '5' and 'h'.

The number 4977 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026906: Number of sums S of distinct positive integers satisfying S <= n.
A055154: Triangle read by rows: T(n,k) = number of k-covers of a labeled n-set, k=1..2^n-1.
A057949: Numbers with more than one factorization into S-primes. See A054520 and A057948 for definition.
A086381: Numbers n such that p=n^2+2 and p+2 are primes.
A122794: Connell (3,2)-sum sequence (partial sums of the (3,2)-Connell sequence).
A193543: E.g.f.: Pi/(sqrt(2)*L) * (1 + 2*Sum_{n>=1} cosh(2*Pi*n*x/L)/cosh(n*Pi)) where L = Lemniscate constant.
A200886: T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors
A203066: T(n,k)=Number of nXk 0..6 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor
A254698: T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having the maximum of some two terms equal to the minimum of the remaining three terms
A325547: Number of compositions of n with strictly increasing differences.

Number of the day: 4918

Properties of the number 4918:

4918 is the 1241^th totient number.
4918 = 2 × 2459 is semiprime and squarefree.
4918 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2458 totatives.
4918 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 4918 results in a sphenic number.
4918 is the difference of 2 positive pentagonal numbers in 2 ways.
4918 = 6² + 11² + 69² is the sum of 3 positive squares.
4918² is the sum of 3 positive squares.
4918 is a proper divisor of 3¹²²⁹ - 1.
4918 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 8, 11, 14, 15, 16, 19, 21, 23, 26, 29, 30, 33, 35, 37, 40, 45, 50, 51, 52, 54, 56, 60, 65, 70, 71, 73, 74, 79, 80, 87, 89, 97, 98, and 100.
4918 is palindromic in (at least) the following bases: -4, and -39.
4918 in base 6 = 34434 and consists of only the digits '3' and '4'.
4918 in base 9 = 6664 and consists of only the digits '4' and '6'.
4918 in base 26 = 774 and consists of only the digits '4' and '7'.
4918 in base 49 = 22I and consists of only the digits '2' and 'I'.

The number 4918 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006137: a(n) = 1 + n/2 + 9*n^2/2.
A084381: a(n) = n^3 + 5.
A089395: Prime productive numbers n: Let the digits of n be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If n is a k-digit number it produces k such primes.
A099411: Numbers n such that 3*R_n + 4 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
A168011: a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2.
A194593: Semiprimes s such that phi(s)/2 is prime.
A204662: Numbers n such that n!8-1 is prime.
A211650: Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 < x^3 + y^3.
A215431: Numbers n such that n^128+(n+1)^128 is a prime.
A285799: Number of partitions of n into parts with an odd number of distinct prime divisors.

Number of the day: 674677

Properties of the number 674677:

674677 is a cyclic number.
674677 is the 54655^th prime.
674677 has 33 antidivisors and 674676 totatives.
674677 has an emirp digit sum 37 in base 10.
674677 has sum of divisors equal to 674678 which is semiprime.
674677 = 337339² - 337338² is the difference of 2 nonnegative squares in 1 way.
674677 is the sum of 2 positive triangular numbers.
674677 is the difference of 2 positive pentagonal numbers in 1 way.
674677 = 314² + 759² is the sum of 2 positive squares in 1 way.
674677 = 30² + 89² + 816² is the sum of 3 positive squares.
674677² = 476652² + 477485² is the sum of 2 positive squares in 1 way.
674677² is the sum of 3 positive squares.
674677 is a proper divisor of 479⁶²⁴⁷ - 1.
674677 = '6' + '74677' is the concatenation of 2 semiprime numbers.
674677 is an emirp in (at least) the following bases: 13, 23, 26, 27, 37, 39, 41, 56, 58, 69, 71, 75, 77, 81, 83, 87, 88, 90, 91, 95, and 100.

Number of the day: 188521

Properties of the number 188521:

188521 is a cyclic number.
188521 = 53 × 3557 is semiprime and squarefree.
188521 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 184912 totatives.
188521 has a semiprime digit sum 25 in base 10.
188521 = 94261² - 94260² = 1805² - 1752² is the difference of 2 nonnegative squares in 2 ways.
188521 is the difference of 2 positive pentagonal numbers in 2 ways.
188521 = 275² + 336² = 140² + 411² is the sum of 2 positive squares in 2 ways.
188521 = 120² + 211² + 360² is the sum of 3 positive squares.
188521² = 99596² + 160065² = 37271² + 184800² = 115080² + 149321² = 65985² + 176596² is the sum of 2 positive squares in 4 ways.
188521² is the sum of 3 positive squares.
188521 is a proper divisor of 1931²⁸ - 1.
188521 is an emirpimes in (at least) the following bases: 3, 4, 5, 7, 9, 11, 13, 17, 18, 22, 29, 33, 38, 40, 45, 46, 47, 49, 50, 51, 57, 59, 62, 66, 69, 71, 75, 79, 81, 82, 83, 85, 91, 98, and 99.
188521 is palindromic in (at least) the following bases: 73, -83, and -88.
188521 in base 57 = 111M and consists of only the digits '1' and 'M'.

Number of the day: 367815

Properties of the number 367815:

367815 = 3 × 5 × 7 × 31 × 113 is the 336445^th composite number and is squarefree.
367815 has 5 distinct prime factors, 32 divisors, 39 antidivisors and 161280 totatives.
367815 has a sphenic digit sum 30 in base 10.
367815 has an oblong digit sum 30 in base 10.
367815 is the difference of 2 nonnegative squares in 16 ways.
367815 is the difference of 2 positive pentagonal numbers in 5 ways.
367815 is not the sum of 3 positive squares.
367815² = 220689² + 294252² = 179676² + 320943² = 257796² + 262353² = 48825² + 364560² is the sum of 2 positive squares in 4 ways.
367815² is the sum of 3 positive squares.
367815 is a proper divisor of 211¹² - 1.
367815 = '36781' + '5' is the concatenation of 2 prime numbers.
367815 is palindromic in (at least) the following bases: 96, and -77.

The number 367815 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A230498: a(n) is the minimal odd odious k>1, such that k^i, i=2,...,n, all are evil, and a(n)=0, if there is no such k.

Number of the day: 42049

Properties of the number 42049:

42049 = 7 × 6007 is semiprime and squarefree.
42049 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 36036 totatives.
42049 has a prime digit sum 19 in base 10.
42049 = 1³ + 14³ + 34³ is the sum of 3 positive cubes in 1 way.
42049 = 21025² - 21024² = 3007² - 3000² is the difference of 2 nonnegative squares in 2 ways.
42049 is the sum of 2 positive triangular numbers.
42049 is the difference of 2 positive pentagonal numbers in 2 ways.
42049 = 12² + 17² + 204² is the sum of 3 positive squares.
42049² is the sum of 3 positive squares.
42049 is a proper divisor of 97²² - 1.
42049 = '4' + '2049' is the concatenation of 2 semiprime numbers.
42049 is an emirpimes in (at least) the following bases: 5, 11, 12, 14, 21, 23, 26, 28, 31, 38, 40, 46, 47, 54, 55, 56, 60, 61, 63, 65, 66, 67, 71, 73, 82, 83, 88, 89, 94, 95, and 99.
42049 is palindromic in (at least) the following bases: 77, -78, and -92.
42049 in base 17 = 8988 and consists of only the digits '8' and '9'.

The number 42049 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008779: Number of n-dimensional partitions of 5.
A041266: Numerators of continued fraction convergents to sqrt(146).
A042118: Numerators of continued fraction convergents to sqrt(584).
A150579: 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, 0, 1), (0, 0, 1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}
A154515: a(n) = 648*n^2 + 72*n + 1.
A157326: a(n) = 10368*n^2 + 288*n + 1.
A157337: a(n) = 128*n^2 + 32*n + 1.
A157433: 128n^2 + 2336n + 10657.
A157919: a(n) = 50*n^2 - 1.
A306973: Numerator of best rational approximation x/y of sqrt(k), y<=k, with k given by A306972. The corresponding denominators are given in A306974.

Number of the day: 7222020

Happy Casual π Day!

Properties of the number 7222020:

7222020 = 2² × 3 × 5 × 13 × 47 × 197 is the 6731306^th composite number and is not squarefree.
7222020 has 6 distinct prime factors, 96 divisors, 35 antidivisors and 1731072 totatives.
7222020 has an emirpimes digit sum 15 in base 10.
7222020 has a triangular digit sum 15 in base 10.
7222020 is the difference of 2 nonnegative squares in 16 ways.
7222020 is the sum of 2 positive triangular numbers.
7222020 is the difference of 2 positive pentagonal numbers in 7 ways.
7222020 = 296² + 350² + 2648² is the sum of 3 positive squares.
7222020² = 5103072² + 5110404² = 4333212² + 5777616² = 3468036² + 6334848² = 2754576² + 6676068² = 1777728² + 6999804² = 764784² + 7181412² = 4513692² + 5637744² = 3666564² + 6222048² = 2744988² + 6680016² = 3697020² + 6204000² = 2777700² + 6666480² = 1801980² + 6993600² = 1026480² + 7148700² is the sum of 2 positive squares in 13 ways.
7222020² is the sum of 3 positive squares.
7222020 is a proper divisor of 1787¹² - 1.

Number of the day: 56303

Properties of the number 56303:

56303 is a cyclic number.
56303 = 13 × 61 × 71 is a sphenic number and squarefree.
56303 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 50400 totatives.
56303 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 56303 results in a semiprime.
56303 = 28152² - 28151² = 2172² - 2159² = 492² - 431² = 432² - 361² is the difference of 2 nonnegative squares in 4 ways.
56303 is the difference of 2 positive pentagonal numbers in 4 ways.
56303 is not the sum of 3 positive squares.
56303² = 21655² + 51972² = 11928² + 55025² = 30672² + 47215² = 10153² + 55380² is the sum of 2 positive squares in 4 ways.
56303² is the sum of 3 positive squares.
56303 is a proper divisor of 853⁴ - 1.
56303 is palindromic in (at least) the following bases: 65, 81, and -59.

The number 56303 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A077060: Smallest k>A077059(n) such that A077059(n)^2+k^2 is a cube (=A077061(n)^3).
A079403: Let G(t) be the set of numbers between 2^(t-1) and 2^t-1, inclusive. There is a unique number a(t) in G(t) so that the denominator of the a(t)-th partial sum of the double harmonic series is divisible by smaller 2-powers than its neighbors.
A187257: Number of UH^jU's for some j>0, where U=(1,1) and H=(1,1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).
A188312: Expansion of (1/(1-x^2))*c(x/((1-x)*(1-x^2))) where c(x) is the g.f. of A000108.
A323266: A323265(n)/2.

Number of the day: 9871

Properties of the number 9871:

9871 is a cyclic number.
9871 is the 1218^th prime.
9871 has 5 antidivisors and 9870 totatives.
9871 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 9871 results in an emirp.
9871 = 4936² - 4935² is the difference of 2 nonnegative squares in 1 way.
9871 is the sum of 2 positive triangular numbers.
9871 is the difference of 2 positive pentagonal numbers in 1 way.
9871 is not the sum of 3 positive squares.
9871² is the sum of 3 positive squares.
9871 is a proper divisor of 419³⁵ - 1.
9871 = '9' + '871' is the concatenation of 2 semiprime numbers.
9871 = '987' + '1' is the concatenation of 2 Fibonacci numbers.
9871 is an emirp in (at least) the following bases: 5, 10, 11, 17, 18, 20, 35, 41, 42, 43, 44, 45, 52, 53, 55, 56, 59, 61, 65, 69, 74, 76, 77, 87, 88, and 93.
9871 is palindromic in (at least) the following bases: 29, 36, 94, and -71.
9871 in base 3 = 111112121 and consists of only the digits '1' and '2'.
9871 in base 21 = 1181 and consists of only the digits '1' and '8'.
9871 in base 29 = blb and consists of only the digits 'b' and 'l'.
9871 in base 36 = 7m7 and consists of only the digits '7' and 'm'.
9871 in base 37 = 77T and consists of only the digits '7' and 'T'.
9871 in base 40 = 66V and consists of only the digits '6' and 'V'.

The number 9871 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007810: Largest prime with n distinct decimal digits.
A030540: Largest n-digit norep emirp.
A053072: Primes p such that p-12, p and p+12 are consecutive primes.
A055469: Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).
A071361: Largest n-digit prime with strictly decreasing digits.
A073102: Primes of the form 210n + 1.
A120160: a(n)=ceiling( sum_{i=1..n-1} a(i)/4), a(1)=1.
A188135: a(n) = 8*n^2 + 2*n + 1.
A188382: Primes of the form 8*n^2 + 2*n + 1.
A267503: Primes n such that n-1 is squarefree and all prime divisors of n-1 other than 5 are in the sequence.

Number of the day: 84889

Properties of the number 84889:

84889 is a cyclic number.
84889 = 7 × 67 × 181 is a sphenic number and squarefree.
84889 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 71280 totatives.
84889 has an emirp digit sum 37 in base 10.
84889 = 7³ + 25³ + 41³ = 28³ + 30³ + 33³ is the sum of 3 positive cubes in 2 ways.
84889 = 42445² - 42444² = 6067² - 6060² = 667² - 600² = 325² - 144² is the difference of 2 nonnegative squares in 4 ways.
84889 is the sum of 2 positive triangular numbers.
84889 is the difference of 2 positive pentagonal numbers in 4 ways.
84889 = 8² + 93² + 276² is the sum of 3 positive squares.
84889² = 8911² + 84420² is the sum of 2 positive squares in 1 way.
84889² is the sum of 3 positive squares.
84889 is a proper divisor of 967⁹ - 1.
84889 in base 45 = ffJ and consists of only the digits 'J' and 'f'.
84889 in base 51 = WWP and consists of only the digits 'P' and 'W'.

The number 84889 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023596: Convolution of A023532 and Fibonacci numbers.
A135214: a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^4 if n is even.
A232704: Numbers n such that sigma(n)+n divides sigma(n^2).
A331763: Number of vertices formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

Number of the day: 718570

Properties of the number 718570:

718570 = 2 × 5 × 181 × 397 is the 660641^th composite number and is squarefree.
718570 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 285120 totatives.
718570 has a triangular digit sum 28 in base 10.
718570 = (258 × 259)/2 + … + (277 × 278)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
718570 is the sum of 2 positive triangular numbers.
718570 is the difference of 2 positive pentagonal numbers in 4 ways.
718570 = 577² + 621² = 177² + 829² = 557² + 639² = 89² + 843² is the sum of 2 positive squares in 4 ways.
718570 = 135² + 172² + 819² is the sum of 3 positive squares.
718570² = 431142² + 574856² = 222992² + 683094² = 22806² + 718208² = 368416² + 616938² = 293466² + 655912² = 52712² + 716634² = 489104² + 526422² = 150054² + 702728² = 98072² + 711846² = 472150² + 541680² = 75430² + 714600² = 348650² + 628320² = 412680² + 588250² is the sum of 2 positive squares in 13 ways.
718570² is the sum of 3 positive squares.
718570 is a proper divisor of 857¹² - 1.
718570 = '7185' + '70' is the concatenation of 2 sphenic numbers.

Number of the day: 7172020

Happy Yellow Pig Day!

Properties of the number 7172020:

7172020 = 2² × 5 × 358601 is the 6684448^th composite number and is not squarefree.
7172020 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2868800 totatives.
7172020 has a prime digit sum 19 in base 10.
7172020 = 1793006² - 1793004² = 358606² - 358596² is the difference of 2 nonnegative squares in 2 ways.
7172020 is the difference of 2 positive pentagonal numbers in 2 ways.
7172020 = 1756² + 2022² = 564² + 2618² is the sum of 2 positive squares in 2 ways.
7172020 = 246² + 280² + 2652² is the sum of 3 positive squares.
7172020² = 4303212² + 5737616² = 2953104² + 6535828² = 1004948² + 7101264² = 3456800² + 6283980² is the sum of 2 positive squares in 4 ways.
7172020² is the sum of 3 positive squares.
7172020 is a proper divisor of 1031³²⁶ - 1.
7172020 in base 3 = 111111101011101 and consists of only the digits '0' and '1'.
7172020 in base 9 = 14441141 and consists of only the digits '1' and '4'.

Number of the day: 85706

Properties of the number 85706:

85706 = 2 × 42853 is semiprime and squarefree.
85706 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 42852 totatives.
85706 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 85706 results in a sphenic number.
85706 = 205² + 209² is the sum of 2 positive squares in 1 way.
85706 = 16² + 65² + 285² is the sum of 3 positive squares.
85706² = 1656² + 85690² is the sum of 2 positive squares in 1 way.
85706² is the sum of 3 positive squares.
85706 is a proper divisor of 59³⁵⁷¹ - 1.
85706 = '85' + '706' is the concatenation of 2 semiprime numbers.
85706 is an emirpimes in (at least) the following bases: 3, 5, 9, 15, 34, 35, 36, 39, 40, 44, 46, 50, 51, 52, 53, 54, 55, 58, 59, 61, 67, 82, 89, and 94.
85706 is palindromic in (at least) the following bases: 62, and 87.
85706 in base 62 = MIM and consists of only the digits 'I' and 'M'.

Number of the day: 90538

Properties of the number 90538:

90538 = 2 × 7 × 29 × 223 is the 81771^th composite number and is squarefree.
90538 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 37296 totatives.
90538 has a semiprime digit sum 25 in base 10.
90538 is the sum of 2 positive triangular numbers.
90538 is the difference of 2 positive pentagonal numbers in 5 ways.
90538 = 9² + 76² + 291² is the sum of 3 positive squares.
90538² = 62440² + 65562² is the sum of 2 positive squares in 1 way.
90538² is the sum of 3 positive squares.
90538 is a proper divisor of 853¹² - 1.
90538 = '905' + '38' is the concatenation of 2 semiprime numbers.
90538 is palindromic in (at least) the following bases: 92, -67, -85, and -96.

The number 90538 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A276901: Number of positive walks with n steps {-3,-2,-1,1,2,3} starting at the origin, ending at altitude 2, and staying strictly above the x-axis.
A278183: Number of n X 2 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
A278188: T(n,k)=Number of nXk 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

Number of the day: 9524

Properties of the number 9524:

9524 = 2² × 2381 is the 8344^th composite number and is not squarefree.
9524 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 4760 totatives.
9524 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 9524 results in a prime.
9524 = (67 × 68)/2 + … + (70 × 71)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
9524 = 2382² - 2380² is the difference of 2 nonnegative squares in 1 way.
9524 is the difference of 2 positive pentagonal numbers in 1 way.
9524 = 68² + 70² is the sum of 2 positive squares in 1 way.
9524 = 32² + 38² + 84² is the sum of 3 positive squares.
9524² = 276² + 9520² is the sum of 2 positive squares in 1 way.
9524² is the sum of 3 positive squares.
9524 is a proper divisor of 1021⁷ - 1.
9524 is palindromic in (at least) the following bases: 69, 89, -22, -29, -56, and -69.
9524 in base 13 = 4448 and consists of only the digits '4' and '8'.
9524 in base 28 = c44 and consists of only the digits '4' and 'c'.
9524 in base 32 = 99k and consists of only the digits '9' and 'k'.
9524 in base 34 = 884 and consists of only the digits '4' and '8'.

The number 9524 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A010008: a(0) = 1, a(n) = 18*n^2 + 2 for n>0.
A050256: Diaconis-Mosteller approximation to the Birthday problem function.
A096374: Number of partitions of n such that the least part occurs with even multiplicity.
A108099: a(n) = 8n^2 + 8n + 4.
A117525: Total sum of parts of multiplicity 2 in all partitions of n.
A175287: Partial sums of ceiling(n^2/4).
A188896: Numbers n such that there is no square n-gonal number greater than 1.
A228646: Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=6.
A229082: Number of circular permutations i_0, i_1, ..., i_n of 0, 1, ..., n such that all the n+1 numbers i_0^2+i_1, i_1^2+i_2, ..., i_{n-1}^2+i_n, i_n^2+i_0 are of the form (p-1)/2 with p an odd prime.
A273362: Numbers n such that the decimal number concat(7,n) is a square.

Number of the day: 7804

Properties of the number 7804:

7804 = 2² × 1951 is the 6816^th composite number and is not squarefree.
7804 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 3900 totatives.
7804 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 7804 results in a semiprime.
7804 = 6³ + 9³ + 19³ is the sum of 3 positive cubes in 1 way.
7804 = 1952² - 1950² is the difference of 2 nonnegative squares in 1 way.
7804 is the difference of 2 positive pentagonal numbers in 1 way.
7804 is not the sum of 3 positive squares.
7804² is the sum of 3 positive squares.
7804 is a proper divisor of 809¹⁰ - 1.
7804 is palindromic in (at least) the following bases: 22, 40, -50, and -83.
7804 in base 11 = 5955 and consists of only the digits '5' and '9'.
7804 in base 22 = g2g and consists of only the digits '2' and 'g'.
7804 in base 24 = dd4 and consists of only the digits '4' and 'd'.
7804 in base 25 = cc4 and consists of only the digits '4' and 'c'.
7804 in base 39 = 554 and consists of only the digits '4' and '5'.
7804 in base 40 = 4Z4 and consists of only the digits '4' and 'Z'.

The number 7804 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014404: Number of ways of getting 5 of a kind, straight flush, 4 of a kind, full house, other flush, other straight, 3 of a kind, 2 pair, a pair or no pair in 5-card poker when joker is wild.
A053080: Number of ways of getting 5 of a kind, royal flush, other straight flush, 4 of a kind, full house, other flush, other straight, 3 of a kind, 2 pair, a pair or no pair in 5-card poker when joker is wild.
A053081: Number of ways of getting no pair, a pair, 2 pair, 3 of a kind, other straight, other flush, full house, 4 of a kind, straight flush or 5 of a kind in 5-card poker when joker is wild.
A078414: a(n) = (a(n-1)+a(n-2))/7^k, where 7^k is the highest power of 7 dividing a(n-1)+a(n-2).
A123284: Number of polyhexes with 24 hexagons, C_(2v) symmetry and containing n carbon atoms.
A153713: Greatest number m such that the fractional part of Pi^A137994(n) <= 1/m.
A153714: Greatest number m such that the fractional part of Pi^A153710(n) <= 1/m.
A256404: Positions of records in A166133.
A283347: T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.
A292741: Number A(n,k) of partitions of n with k sorts of part 1; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Number of the day: 7318

Properties of the number 7318:

7318 = 2 × 3659 is semiprime and squarefree.
7318 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 3658 totatives.
7318 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 7318 results in an emirpimes.
7318 is the sum of 2 positive triangular numbers.
7318 is the difference of 2 positive pentagonal numbers in 2 ways.
7318 = 9² + 26² + 81² is the sum of 3 positive squares.
7318² is the sum of 3 positive squares.
7318 is a proper divisor of 557³¹ - 1.
7318 is an emirpimes in (at least) the following bases: 3, 5, 6, 8, 10, 13, 15, 17, 21, 22, 23, 25, 27, 31, 32, 36, 41, 47, 52, 55, 56, 61, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 88, 94, 95, and 98.
7318 is palindromic in (at least) the following bases: 20, 59, -28, -46, -55, and -62.
7318 in base 3 = 101001001 and consists of only the digits '0' and '1'.
7318 in base 11 = 5553 and consists of only the digits '3' and '5'.
7318 in base 20 = i5i and consists of only the digits '5' and 'i'.
7318 in base 27 = a11 and consists of only the digits '1' and 'a'.
7318 in base 28 = 99a and consists of only the digits '9' and 'a'.
7318 in base 58 = 2AA and consists of only the digits '2' and 'A'.
7318 in base 59 = 262 and consists of only the digits '2' and '6'.

The number 7318 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001372: Number of mappings (or mapping patterns) from n points to themselves; number of endofunctions.
A042161: Denominators of continued fraction convergents to sqrt(605).
A046746: Sum of smallest parts of all partitions of n.
A141689: Average of Eulerian numbers (A008292) and Pascal's triangle (A007318): t(n,m) = (A008292(n,m) + A007318(n,m))/2.
A212069: Number of (w,x,y,z) with all terms in {1,...,n} and 3*w = x+y+z.
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.
A278616: Sum of terms in level n of TRIP -Stern sequence associated with permutation triple (e,13,132).
A323530: Number of square plane partitions of n with strictly decreasing rows and columns.
A325882: Bases b where exactly six primes p with p < b exist such that p is a base-b Wieferich prime.

Number of the day: 49675

Properties of the number 49675:

49675 = 5² × 1987 is the 44572^th composite number and is not squarefree.
49675 has 2 distinct prime factors, 6 divisors, 27 antidivisors and 39720 totatives.
49675 has an emirp digit sum 31 in base 10.
49675 = 24838² - 24837² = 4970² - 4965² = 1006² - 981² is the difference of 2 nonnegative squares in 3 ways.
49675 is the sum of 2 positive triangular numbers.
49675 is the difference of 2 positive pentagonal numbers in 3 ways.
49675 = 25² + 33² + 219² is the sum of 3 positive squares.
49675² = 29805² + 39740² = 13909² + 47688² is the sum of 2 positive squares in 2 ways.
49675² is the sum of 3 positive squares.
49675 is a proper divisor of 647⁶⁰ - 1.
49675 = '4967' + '5' is the concatenation of 2 prime numbers.
49675 is palindromic in (at least) base -62.
49675 in base 47 = MMh and consists of only the digits 'M' and 'h'.
49675 in base 61 = DLL and consists of only the digits 'D' and 'L'.

Number of the day: 9422

Properties of the number 9422:

9422 = 2 × 7 × 673 is a sphenic number and squarefree.
9422 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4032 totatives.
9422 has an emirp digit sum 17 in base 10.
9422 has a Fibonacci digit product 144 in base 10.
Reversing the decimal digits of 9422 results in a semiprime.
9422 = 2² + 3² + 97² is the sum of 3 positive squares.
9422² = 5390² + 7728² is the sum of 2 positive squares in 1 way.
9422² is the sum of 3 positive squares.
9422 is a proper divisor of 929⁶ - 1.
9422 = '9' + '422' is the concatenation of 2 semiprime numbers.
9422 is palindromic in (at least) the following bases: 35, 43, and 60.
9422 in base 12 = 5552 and consists of only the digits '2' and '5'.
9422 in base 35 = 7o7 and consists of only the digits '7' and 'o'.
9422 in base 42 = 5EE and consists of only the digits '5' and 'E'.
9422 in base 43 = 545 and consists of only the digits '4' and '5'.
9422 in base 48 = 44E and consists of only the digits '4' and 'E'.
9422 in base 59 = 2ff and consists of only the digits '2' and 'f'.
9422 in base 60 = 2b2 and consists of only the digits '2' and 'b'.

The number 9422 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A091434: Poincar series [or Poincare series] (or Molien series) for a certain four-fold wreath product P_4.
A116271: n times n+9 gives the concatenation of two numbers m and m-3.
A173337: Numbers k>1 such that phi(phi(k))= sigma(sopf(k)).
A196507: a(n) = n*(3*n^2 + 6*n + 1).
A208483: Total sum of the sums of all positive k-th ranks of all partitions of n.
A224197: Least b > p_n^2 such that [p_1^2,p_2^2,...,p_n^2] in base b is prime, where p_j denotes the j-th prime.
A232359: Positions of peak values in A232221.
A248690: Number of words in the n-th book of the King James Version of the Holy Bible.
A272675: Indices where records occur in A265432.
A290574: Self numbers that are the product of two self numbers greater than one.

Number of the day: 394417

Properties of the number 394417:

394417 is a cyclic number.
394417 = 17 × 23201 is semiprime and squarefree.
394417 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 371200 totatives.
394417 has a triangular digit sum 28 in base 10.
394417 = 197209² - 197208² = 11609² - 11592² is the difference of 2 nonnegative squares in 2 ways.
394417 is the sum of 2 positive triangular numbers.
394417 is the difference of 2 positive pentagonal numbers in 2 ways.
394417 = 231² + 584² = 71² + 624² is the sum of 2 positive squares in 2 ways.
394417 = 143² + 168² + 588² is the sum of 3 positive squares.
394417² = 269808² + 287695² = 185608² + 348015² = 88608² + 384335² = 102680² + 380817² is the sum of 2 positive squares in 4 ways.
394417² is the sum of 3 positive squares.
394417 is a proper divisor of 157¹⁰⁰ - 1.
394417 = '39' + '4417' is the concatenation of 2 semiprime numbers.
394417 is an emirpimes in (at least) the following bases: 2, 6, 12, 13, 17, 19, 20, 21, 22, 27, 29, 30, 35, 37, 38, 40, 41, 43, 60, 62, 65, 66, 70, 72, 74, 79, 84, 85, 86, 87, 89, 94, 97, 98, 99, and 100.
394417 in base 27 = k111 and consists of only the digits '1' and 'k'.

Number of the day: 76700

Henri Cartan was born on this day 116 years ago.

Properties of the number 76700:

76700 = 2² × 5² × 13 × 59 is the 69156^th composite number and is not squarefree.
76700 has 4 distinct prime factors, 36 divisors, 15 antidivisors and 27840 totatives.
76700 has an oblong digit sum 20 in base 10.
76700 = 19176² - 19174² = 3840² - 3830² = 1488² - 1462² = 792² - 742² = 384² - 266² = 360² - 230² is the difference of 2 nonnegative squares in 6 ways.
76700 is the difference of 2 positive pentagonal numbers in 6 ways.
76700 is not the sum of 3 positive squares.
76700² = 46020² + 61360² = 18880² + 74340² = 38940² + 66080² = 29500² + 70800² = 21476² + 73632² = 8496² + 76228² = 48144² + 59708² is the sum of 2 positive squares in 7 ways.
76700² is the sum of 3 positive squares.
76700 is a proper divisor of 827²⁰ - 1.
76700 in base 18 = d2d2 and consists of only the digits '2' and 'd'.

Number of the day: 471090544

Properties of the number 471090544:

471090544 = 2⁴ × 29443159 is the 446180180^th composite number and is not squarefree.
471090544 has 2 distinct prime factors, 10 divisors, 37 antidivisors and 235545264 totatives.
471090544 has a semiprime digit sum 34 in base 10.
471090544 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 471090544 results in a sphenic number.
471090544 = 117772637² - 117772635² = 58886320² - 58886316² = 29443163² - 29443155² is the difference of 2 nonnegative squares in 3 ways.
471090544 is the difference of 2 positive pentagonal numbers in 1 way.
471090544 is not the sum of 3 positive squares.
471090544² is the sum of 3 positive squares.
471090544 is a proper divisor of 1021²²⁰⁵⁴⁸ - 1.

Number of the day: 3475

Properties of the number 3475:

3475 = 5² × 139 is the 2987^th composite number and is not squarefree.
3475 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 2760 totatives.
3475 has a prime digit sum 19 in base 10.
3475 has an oblong digit product 420 in base 10.
Reversing the decimal digits of 3475 results in a prime.
3475 = 1738² - 1737² = 350² - 345² = 82² - 57² is the difference of 2 nonnegative squares in 3 ways.
3475 is the sum of 2 positive triangular numbers.
3475 is the difference of 2 positive pentagonal numbers in 3 ways.
3475 = 1² + 15² + 57² is the sum of 3 positive squares.
3475² = 2085² + 2780² = 973² + 3336² is the sum of 2 positive squares in 2 ways.
3475² is the sum of 3 positive squares.
3475 is a proper divisor of 557⁴ - 1.
3475 = '347' + '5' is the concatenation of 2 prime numbers.
3475 is palindromic in (at least) base 31.
3475 in base 30 = 3pp and consists of only the digits '3' and 'p'.
3475 in base 31 = 3j3 and consists of only the digits '3' and 'j'.
3475 in base 41 = 22V and consists of only the digits '2' and 'V'.
3475 in base 58 = 11r and consists of only the digits '1' and 'r'.

Number of the day: 433355

Properties of the number 433355:

433355 is a cyclic number.
433355 = 5 × 13 × 59 × 113 is the 396922^th composite number and is squarefree.
433355 has 4 distinct prime factors, 16 divisors, 41 antidivisors and 311808 totatives.
433355 has a prime digit sum 23 in base 10.
433355 = 216678² - 216677² = 43338² - 43333² = 16674² - 16661² = 3702² - 3643² = 3366² - 3301² = 1974² - 1861² = 882² - 587² = 666² - 101² is the difference of 2 nonnegative squares in 8 ways.
433355 is the difference of 2 positive pentagonal numbers in 6 ways.
433355 = 5² + 41² + 657² is the sum of 3 positive squares.
433355² = 260013² + 346684² = 211692² + 378131² = 303732² + 309101² = 106672² + 420021² = 49973² + 430464² = 161483² + 402144² = 220011² + 373352² = 168504² + 399253² = 267624² + 340843² = 166675² + 400020² = 112100² + 418605² = 218300² + 374355² = 57525² + 429520² is the sum of 2 positive squares in 13 ways.
433355² is the sum of 3 positive squares.
433355 is a proper divisor of 1061⁸ - 1.
433355 = '4333' + '55' is the concatenation of 2 semiprime numbers.

Number of the day: 485480

Properties of the number 485480:

485480 = 2³ × 5 × 53 × 229 is the 445065^th composite number and is not squarefree.
485480 has 4 distinct prime factors, 32 divisors, 13 antidivisors and 189696 totatives.
485480 has a prime digit sum 29 in base 10.
485480 = 121371² - 121369² = 60687² - 60683² = 24279² - 24269² = 12147² - 12127² = 2343² - 2237² = 1251² - 1039² = 759² - 301² = 723² - 193² is the difference of 2 nonnegative squares in 8 ways.
485480 is the difference of 2 positive pentagonal numbers in 3 ways.
485480 = 466² + 518² = 314² + 622² = 122² + 686² = 62² + 694² is the sum of 2 positive squares in 4 ways.
485480 = 14² + 160² + 678² is the sum of 3 positive squares.
485480² = 298496² + 382872² = 291288² + 388384² = 179352² + 451136² = 288288² + 390616² = 175872² + 452504² = 51168² + 482776² = 167384² + 455712² = 42136² + 483648² = 86056² + 477792² = 330600² + 355520² = 256480² + 412200² = 139520² + 465000² = 127200² + 468520² is the sum of 2 positive squares in 13 ways.
485480² is the sum of 3 positive squares.
485480 is a proper divisor of 107⁴ - 1.
485480 is palindromic in (at least) the following bases: 39, and -16.
485480 in base 39 = 8778 and consists of only the digits '7' and '8'.