Number of the day: 609697

René Descartes was born on this day 425 years ago.

Properties of the number 609697:

609697 is a cyclic number.
609697 = 11 × 43 × 1289 is a sphenic number and squarefree.
609697 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 540960 totatives.
609697 has an emirp digit sum 37 in base 10.
609697 = 304849² - 304848² = 27719² - 27708² = 7111² - 7068² = 881² - 408² is the difference of 2 nonnegative squares in 4 ways.
609697 is the difference of 2 positive pentagonal numbers in 3 ways.
609697 = 1² + 36² + 780² is the sum of 3 positive squares.
609697² = 264880² + 549153² is the sum of 2 positive squares in 1 way.
609697² is the sum of 3 positive squares.
609697 is a proper divisor of 419⁵⁶ - 1.
609697 in base 39 = AAXA and consists of only the digits 'A' and 'X'.

Number of the day: 9487

Stefan Banach was born on this day 129 years ago.

Properties of the number 9487:

9487 is a cyclic number.
9487 = 53 × 179 is semiprime and squarefree.
9487 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 9256 totatives.
9487 has a triangular digit sum 28 in base 10.
9487 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 9487 results in an emirpimes.
9487 = 4744² - 4743² = 116² - 63² is the difference of 2 nonnegative squares in 2 ways.
9487 is the sum of 2 positive triangular numbers.
9487 is the difference of 2 positive pentagonal numbers in 1 way.
9487 is not the sum of 3 positive squares.
9487² = 5012² + 8055² is the sum of 2 positive squares in 1 way.
9487² is the sum of 3 positive squares.
9487 is a proper divisor of 1789²⁶ - 1.
9487 = '94' + '87' is the concatenation of 2 semiprime numbers.
9487 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 7, 9, 10, 11, 15, 18, 20, 21, 23, 25, 27, 31, 34, 36, 39, 42, 43, 50, 51, 55, 56, 59, 61, 65, 67, 68, 70, 71, 73, 75, 76, 79, 88, 89, 91, 95, 96, 97, 98, 99, and 100.
9487 is palindromic in (at least) base 93.
9487 in base 3 = 111000101 and consists of only the digits '0' and '1'.
9487 in base 43 = 55R and consists of only the digits '5' and 'R'.

The number 9487 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011942: [ n(n-1)(n-2)(n-3)/32 ].
A020419: Numbers n such that continued fraction for sqrt(n) has period 80.
A022767: Ordered sequence of distinct terms of the form floor(Pi^i * floor(Pi^j)), i, j >= 0.
A031799: Period of continued fraction for sqrt(n) contains exactly 31 ones.
A035076: a(n) is root of square starting with digit 9: first term of runs.
A041540: Numerators of continued fraction convergents to sqrt(287).
A081490: Leading term of n-th row of A081491.
A194268: 8*n^2 + 7*n + 1.
A240733: Floor(6^n/(2+2*cos(Pi/9))^n).
A336561: Numbers k at which point A336459(k) appears multiplicative, but A051027(k) does not.

Number of the day: 17126756

Wilhelm Ackermann was born on this day 125 years ago.

Properties of the number 17126756:

17126756 = 2² × 31 × 59 × 2341 is the 16027811^th composite number and is not squarefree.
17126756 has 4 distinct prime factors, 24 divisors, 23 antidivisors and 8143200 totatives.
17126756 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 17126756 results in a sphenic number.
17126756 = 4281690² - 4281688² = 138150² - 138088² = 72630² - 72512² = 4170² - 512² is the difference of 2 nonnegative squares in 4 ways.
17126756 is the difference of 2 positive pentagonal numbers in 4 ways.
17126756 = 84² + 494² + 4108² is the sum of 3 positive squares.
17126756² = 10096080² + 13834556² is the sum of 2 positive squares in 1 way.
17126756² is the sum of 3 positive squares.
17126756 is a proper divisor of 709¹³⁰ - 1.

Number of the day: 13422

Alexander Grothendieck was born on this day 93 years ago.

Properties of the number 13422:

13422 = 2 × 3 × 2237 is a sphenic number and squarefree.
13422 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 4472 totatives.
13422 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 13422 results in a semiprime.
13422 is the sum of 2 positive triangular numbers.
13422 is the difference of 2 positive pentagonal numbers in 2 ways.
13422 = 1² + 14² + 115² is the sum of 3 positive squares.
13422² = 6072² + 11970² is the sum of 2 positive squares in 1 way.
13422² is the sum of 3 positive squares.
13422 is a proper divisor of 1021⁴ - 1.
13422 = '134' + '22' is the concatenation of 2 semiprime numbers.
13422 is palindromic in (at least) the following bases: 63, -25, -32, and -71.
13422 in base 62 = 3UU and consists of only the digits '3' and 'U'.

The number 13422 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057534: a(n+1) = a(n)/2 if 2|a(n), a(n)/3 if 3|a(n), a(n)/5 if 5|a(n), a(n)/7 if 7|a(n), a(n)/11 if 11|a(n), a(n)/13 if 13|a(n), otherwise 17*a(n)+1.
A059466: Numbers which are the sum of their proper divisors containing the digit 7.
A090744: Consider numbers of the form ...53197531975319753, whose digits read from the right are 3,5,7,9,1,3,5,7,9,1,3,... Sequence gives lengths of these numbers that are primes.
A152232: Similar to A072921 but starting with 3.
A200774: Number of nX5 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
A200777: T(n,k)=Number of nXk 0..2 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other
A211749: Number of -3..3 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four, six or eight distinct values for every i,j,k<=n
A227953: Smallest m such that A070965(m) = n.
A228963: Smallest sets of 6 consecutive abundant numbers in arithmetic progression. The initial abundant number is listed.
A329665: Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.

Number of the day: 922514

Properties of the number 922514:

922514 = 2 × 461257 is semiprime and squarefree.
922514 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 461256 totatives.
922514 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 922514 results in an emirpimes.
922514 = 505² + 817² is the sum of 2 positive squares in 1 way.
922514 = 23² + 48² + 959² is the sum of 3 positive squares.
922514² = 412464² + 825170² is the sum of 2 positive squares in 1 way.
922514² is the sum of 3 positive squares.
922514 is a proper divisor of 107¹⁹²¹⁹ - 1.
922514 = '9' + '22514' is the concatenation of 2 semiprime numbers.
922514 is an emirpimes in (at least) the following bases: 2, 8, 10, 11, 14, 21, 25, 27, 28, 29, 30, 31, 34, 44, 56, 57, 67, 71, 80, 84, 92, 93, 96, 98, and 99.

Number of the day: 4781

Paul Erös was born on this day 108 years ago.

Properties of the number 4781:

4781 is a cyclic number.
4781 = 7 × 683 is semiprime and squarefree.
4781 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 4092 totatives.
4781 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 4781 results in an emirpimes.
4781 = 2391² - 2390² = 345² - 338² is the difference of 2 nonnegative squares in 2 ways.
4781 is the sum of 2 positive triangular numbers.
4781 is the difference of 2 positive pentagonal numbers in 2 ways.
4781 = 6² + 11² + 68² is the sum of 3 positive squares.
4781² is the sum of 3 positive squares.
4781 is a proper divisor of 1367³ - 1.
4781 = '4' + '781' is the concatenation of 2 semiprime numbers.
4781 is an emirpimes in (at least) the following bases: 3, 5, 9, 10, 11, 12, 14, 15, 16, 20, 21, 28, 29, 31, 40, 41, 43, 44, 49, 50, 53, 54, 55, 59, 63, 64, 65, 67, 70, 74, 80, 81, 83, 85, 88, 90, 91, 95, 96, and 98.
4781 is palindromic in (at least) the following bases: -2, and -59.
4781 in base 34 = 44l and consists of only the digits '4' and 'l'.

The number 4781 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000100: a(n) is the number of compositions of n in which the maximal part is 3.
A005424: Smallest number that requires n iterations of the bi-unitary totient function (A116550) to reach 1.
A025415: Least sum of 3 distinct nonzero squares in exactly n ways.
A092666: a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with 0 < x_1 <= ... <= x_k = n.
A116459: Numbers n such that the minimal length of the corresponding shortest addition chain A003313(n)=A003313(3*n).
A140749: Table c(n,k) of the numerators of coefficients [x^k] P(n,x) of the polynomials P(n,x) of A129891.
A240495: Number of partitions p of n such that the multiplicity of (max(p) - min(p)) is a part.
A244803: The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.
A257462: Number A(n,k) of factorizations of m^n into n factors, where m is a product of exactly k distinct primes and each factor is a product of k primes (counted with multiplicity); square array A(n,k), n>=0, k>=0, read by antidiagonals.
A300937: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Number of the day: 424514

Properties of the number 424514:

424514 = 2 × 31 × 41 × 167 is the 388774^th composite number and is squarefree.
424514 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 199200 totatives.
424514 has an oblong digit sum 20 in base 10.
424514 = 16² + … + 108² is the sum of at least 2 consecutive positive squares in 1 way.
424514 is the difference of 2 positive pentagonal numbers in 3 ways.
424514 = 8² + 57² + 649² is the sum of 3 positive squares.
424514² = 93186² + 414160² is the sum of 2 positive squares in 1 way.
424514² is the sum of 3 positive squares.
424514 is a proper divisor of 1669¹²⁰ - 1.
424514 = '42' + '4514' is the concatenation of 2 sphenic numbers.

The number 424514 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115080: Triangle, read by rows, where T(n,k) equals the dot product of the vector of terms in row n that are to the right of T(n,k) with the vector of terms in column k that are above T(n,k): T(n,k) = Sum_{j=0..n-k-1} T(n,j+k+1)*T(j+k,k) for n>k+1>0, with T(n,n) = 1 and T(n,n-1) = n (n>=1).
A115081: Column 0 of triangle A115080.

Number of the day: 9992109

Joseph Liouville was born on this day 212 years ago.

Properties of the number 9992109:

9992109 = 3 × 37 × 90019 is a sphenic number and squarefree.
9992109 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 6481296 totatives.
9992109 has an emirpimes digit sum 39 in base 10.
Reversing the decimal digits of 9992109 results in a sphenic number.
9992109 = 4996055² - 4996054² = 1665353² - 1665350² = 135047² - 135010² = 45065² - 44954² is the difference of 2 nonnegative squares in 4 ways.
9992109 is the sum of 2 positive triangular numbers.
9992109 is the difference of 2 positive pentagonal numbers in 2 ways.
9992109 = 208² + 227² + 3146² is the sum of 3 positive squares.
9992109² = 3240684² + 9451995² is the sum of 2 positive squares in 1 way.
9992109² is the sum of 3 positive squares.
9992109 is a proper divisor of 1231⁹ - 1.
9992109 = '9' + '992109' is the concatenation of 2 semiprime numbers.

Number of the day: 11111

Pierre-Simon Laplace was born on this day 272 years ago.

Emmy Noether was born on this day 139 years ago.

Properties of the number 11111:

11111 is a cyclic number.
11111 = 41 × 271 is semiprime and squarefree.
11111 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 10800 totatives.
11111 has a prime digit sum 5 in base 10.
11111 has a Fibonacci digit sum 5 in base 10.
11111 has a Fibonacci digit product 1 in base 10.
11111 has a triangular digit product 1 in base 10.
11111 = 5556² - 5555² = 156² - 115² is the difference of 2 nonnegative squares in 2 ways.
11111 is the difference of 2 positive pentagonal numbers in 2 ways.
11111 is not the sum of 3 positive squares.
11111² = 2439² + 10840² is the sum of 2 positive squares in 1 way.
11111² is the sum of 3 positive squares.
11111 is a proper divisor of 1439¹⁰ - 1.
11111 is an emirpimes in (at least) the following bases: 3, 5, 8, 11, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 35, 39, 43, 44, 49, 51, 53, 54, 55, 56, 58, 61, 65, 66, 67, 75, 77, 79, 81, 84, 85, 86, 87, 89, 96, 99, and 100.
11111 is a palindrome (in base 10).
11111 is palindromic in (at least) base 69.
11111 consists of only the digit '1'.

The number 11111 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000042: Unary representation of natural numbers.
A002275: Repunits: (10^n - 1)/9. Often denoted by R_n.
A002778: Numbers whose square is a palindrome.
A004676: Primes written in base 2.
A007088: The binary numbers (or binary words, or binary vectors): numbers written in base 2.
A007931: Numbers that contain only 1's and 2's. Nonempty binary strings of length n in lexicographic order.
A010785: Repdigit numbers, or numbers with repeated digits.
A039724: Numbers in base -2.
A053699: a(n) = n^4 + n^3 + n^2 + n + 1.
A057148: Palindromes only using 0 and 1 (i.e., base 2 palindromes).

Number of the day: 51371

Properties of the number 51371:

51371 is a cyclic number.
51371 = 47 × 1093 is semiprime and squarefree.
51371 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 50232 totatives.
51371 has an emirp digit sum 17 in base 10.
51371 has a sphenic digit product 105 in base 10.
51371 has a triangular digit product 105 in base 10.
Reversing the decimal digits of 51371 results in an emirpimes.
51371 = 25686² - 25685² = 570² - 523² is the difference of 2 nonnegative squares in 2 ways.
51371 is the difference of 2 positive pentagonal numbers in 2 ways.
51371 = 11² + 25² + 225² is the sum of 3 positive squares.
51371² = 6204² + 50995² is the sum of 2 positive squares in 1 way.
51371² is the sum of 3 positive squares.
51371 is a proper divisor of 941³ - 1.
51371 = '51' + '371' is the concatenation of 2 semiprime numbers.
51371 is an emirpimes in (at least) the following bases: 4, 5, 6, 7, 10, 11, 14, 23, 24, 27, 33, 34, 36, 37, 38, 39, 43, 44, 49, 52, 58, 59, 60, 62, 66, 67, 81, 82, 83, 84, 85, 88, 89, 92, and 94.
51371 is palindromic in (at least) the following bases: 54, -45, and -50.
51371 in base 42 = T55 and consists of only the digits '5' and 'T'.
51371 in base 44 = QNN and consists of only the digits 'N' and 'Q'.
51371 in base 49 = LJJ and consists of only the digits 'J' and 'L'.
51371 in base 54 = HXH and consists of only the digits 'H' and 'X'.
51371 in base 58 = FFf and consists of only the digits 'F' and 'f'.

The number 51371 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008384: Crystal ball sequence for A_4 lattice.
A234729: Volume of right regular hexagonal pyramid with height and side lengths n, rounded down.

Number of the day: 70881

Joseph Fourier was born on this day 253 years ago.

George David Birkhoff was born on this day 137 years ago.

Properties of the number 70881:

70881 is a cyclic number.
70881 = 3 × 23627 is semiprime and squarefree.
70881 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 47252 totatives.
Reversing the decimal digits of 70881 results in an emirpimes.
70881 = 35441² - 35440² = 11815² - 11812² is the difference of 2 nonnegative squares in 2 ways.
70881 is the difference of 2 positive pentagonal numbers in 1 way.
70881 = 11² + 46² + 262² is the sum of 3 positive squares.
70881² is the sum of 3 positive squares.
70881 is a proper divisor of 19¹¹⁸¹³ - 1.
70881 is an emirpimes in (at least) the following bases: 3, 6, 9, 10, 19, 21, 28, 31, 34, 35, 36, 42, 43, 45, 49, 53, 55, 63, 69, 71, 72, 75, 80, 83, 88, 90, and 100.
70881 in base 55 = NNf and consists of only the digits 'N' and 'f'.

Number of the day: 77737

Alfréd Rényi was born on this day 100 years ago.

Properties of the number 77737:

77737 is a cyclic number.
77737 = 11 × 37 × 191 is a sphenic number and squarefree.
77737 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 68400 totatives.
77737 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 77737 results in a sphenic number.
77737 = 38869² - 38868² = 3539² - 3528² = 1069² - 1032² = 299² - 108² is the difference of 2 nonnegative squares in 4 ways.
77737 is the sum of 2 positive triangular numbers.
77737 is the difference of 2 positive pentagonal numbers in 3 ways.
77737 = 42² + 97² + 258² is the sum of 3 positive squares.
77737² = 25212² + 73535² is the sum of 2 positive squares in 1 way.
77737² is the sum of 3 positive squares.
77737 is a proper divisor of 1153²⁰ - 1.
77737 = '77' + '737' is the concatenation of 2 semiprime numbers.
77737 is palindromic in (at least) base 67.
77737 consists of only the digits '3' and '7'.

The number 77737 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A043520: Numbers such that the number of 7's in their decimal representation is 4.

Number of the day: 6892

Properties of the number 6892:

6892 = 2² × 1723 is the 6005^th composite number and is not squarefree.
6892 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 3444 totatives.
6892 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 6892 results in a semiprime.
6892 = 1724² - 1722² is the difference of 2 nonnegative squares in 1 way.
6892 is the difference of 2 positive pentagonal numbers in 1 way.
6892 = 18² + 22² + 78² is the sum of 3 positive squares.
6892² is the sum of 3 positive squares.
6892 is a proper divisor of 41³ - 1.
6892 is palindromic in (at least) the following bases: 41, 53, -42, and -65.
6892 in base 40 = 4CC and consists of only the digits '4' and 'C'.
6892 in base 41 = 444 and consists of only the digit '4'.
6892 in base 52 = 2SS and consists of only the digits '2' and 'S'.
6892 in base 53 = 2O2 and consists of only the digits '2' and 'O'.
6892 in base 58 = 22m and consists of only the digits '2' and 'm'.

The number 6892 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020169: Pseudoprimes to base 41.
A079104: Number of permutations of length n containing the minimum number of monotone subsequences of length 4.
A079105: Number of permutations of length n, in which all monotone subsequences of length 4 are descending or all such subsequences are ascending, containing the minimum number of such subsequences subject to that constraint.
A103198: Number of compositions of n into a square number of parts.
A112087: 4*(n^2 - n + 1).
A130442: Even pseudoprimes to base 41.
A192531: Monotonic ordering of set S generated by these rules:if x and y are in S then 3xy-2x-2y is in S, and 2 is in S.
A212579: Number of (w,x,y,z) with all terms in {1,...,n} and min{|w-x|,|w-y|}=min{|x-y|,|x-z|}.
A263149: Expansion of Product_{k>=1} (1 + x^(2*k+1))^k.
A280611: Number of degree n products of distinct cyclotomic polynomials.

Number of the day: 668

Christian Goldbach was born on this day 331 years ago.

Properties of the number 668:

668 = 2² × 167 is the 546^th composite number and is not squarefree.
668 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 332 totatives.
668 has an oblong digit sum 20 in base 10.
668 has sum of divisors equal to 1176 which is a triangular number.
Reversing the decimal digits of 668 results in a semiprime.
668 = 168² - 166² is the difference of 2 nonnegative squares in 1 way.
668 is the difference of 2 positive pentagonal numbers in 1 way.
668 is not the sum of 3 positive squares.
668² is the sum of 3 positive squares.
668 is a proper divisor of 1669² - 1.
668 is palindromic in (at least) the following bases: 18, 23, and -29.
668 in base 3 = 220202 and consists of only the digits '0' and '2'.
668 in base 9 = 822 and consists of only the digits '2' and '8'.
668 consists of only the digits '6' and '8'.
668 in base 11 = 558 and consists of only the digits '5' and '8'.
668 in base 17 = 255 and consists of only the digits '2' and '5'.
668 in base 18 = 212 and consists of only the digits '1' and '2'.
668 in base 22 = 188 and consists of only the digits '1' and '8'.
668 in base 23 = 161 and consists of only the digits '1' and '6'.
668 in base 25 = 11i and consists of only the digits '1' and 'i'.

The number 668 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000009: Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts.
A005823: Numbers whose ternary expansion contains no 1's.
A026769: Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; T(2,1)=2; for n >= 3 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if 1<=k<=(n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
A051225: Numbers m such that the Bernoulli number B_{2*m} has denominator 30.
A051226: Numbers m such that the Bernoulli number B_m has denominator 30.
A080054: G.f.: Product_{n >= 0} (1+x^(2n+1))/(1-x^(2n+1)).
A143823: Number of subsets {x(1),x(2),...,x(k)} of {1,2,...,n} such that all differences |x(i)-x(j)| are distinct.
A161330: Snowflake (or E-toothpick) sequence (see Comments lines for definition).
A161424: Numbers k whose largest divisor <= sqrt(k) equals 4.
A235229: Numbers whose sum of digits is 20.

Number of the day: 793290

Properties of the number 793290:

793290 = 2 × 3 × 5 × 31 × 853 is the 729837^th composite number and is squarefree.
793290 has 5 distinct prime factors, 32 divisors, 17 antidivisors and 204480 totatives.
793290 has a sphenic digit sum 30 in base 10.
793290 has an oblong digit sum 30 in base 10.
793290 is the sum of 2 positive triangular numbers.
793290 is the difference of 2 positive pentagonal numbers in 4 ways.
793290 = 37² + 40² + 889² is the sum of 3 positive squares.
793290² = 475974² + 634632² = 309504² + 730422² = 501642² + 614544² = 190650² + 770040² is the sum of 2 positive squares in 4 ways.
793290² is the sum of 3 positive squares.
793290 is a proper divisor of 1373⁶⁰ - 1.

Number of the day: 90563

Properties of the number 90563:

90563 is a cyclic number.
90563 = 11 × 8233 is semiprime and squarefree.
90563 has 2 distinct prime factors, 4 divisors, 51 antidivisors and 82320 totatives.
90563 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 90563 results in an emirpimes.
90563 = 45282² - 45281² = 4122² - 4111² is the difference of 2 nonnegative squares in 2 ways.
90563 is the difference of 2 positive pentagonal numbers in 2 ways.
90563 = 15² + 67² + 293² is the sum of 3 positive squares.
90563² = 39875² + 81312² is the sum of 2 positive squares in 1 way.
90563² is the sum of 3 positive squares.
90563 is a proper divisor of 353⁵⁶ - 1.
90563 is an emirpimes in (at least) the following bases: 4, 7, 8, 9, 10, 11, 15, 16, 20, 23, 26, 29, 30, 33, 36, 38, 46, 51, 53, 55, 59, 60, 63, 64, 68, 71, 73, 76, 79, 89, 91, 95, and 96.
90563 is palindromic in (at least) the following bases: 88, and -47.

The number 90563 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A229257: O.g.f.: Sum_{n>=0} x^n / Product_{k=1..n} (1 - n^2*k*x).

Number of the day: 661057

Properties of the number 661057:

661057 is a cyclic number.
661057 = 61 × 10837 is semiprime and squarefree.
661057 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 650160 totatives.
661057 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 661057 results in an emirpimes.
661057 = 330529² - 330528² = 5449² - 5388² is the difference of 2 nonnegative squares in 2 ways.
661057 is the difference of 2 positive pentagonal numbers in 2 ways.
661057 = 264² + 769² = 121² + 804² is the sum of 2 positive squares in 2 ways.
661057 = 14² + 69² + 810² is the sum of 3 positive squares.
661057² = 194568² + 631775² = 119207² + 650220² = 406032² + 521665² = 305305² + 586332² is the sum of 2 positive squares in 4 ways.
661057² is the sum of 3 positive squares.
661057 is a proper divisor of 367²⁵² - 1.
661057 is an emirpimes in (at least) the following bases: 7, 10, 11, 12, 17, 19, 25, 26, 28, 29, 31, 33, 37, 44, 45, 48, 50, 53, 55, 59, 64, 67, 69, 70, 74, 76, 78, 79, 80, 83, 85, 88, 91, 92, 93, 95, and 100.
661057 is palindromic in (at least) base -18.
661057 in base 60 = 33bb and consists of only the digits '3' and 'b'.

Number of the day: 480424

Properties of the number 480424:

480424 = 2³ × 7 × 23 × 373 is the 440383^th composite number and is not squarefree.
480424 has 4 distinct prime factors, 32 divisors, 23 antidivisors and 196416 totatives.
480424 has a semiprime digit sum 22 in base 10.
480424 = 120107² - 120105² = 60055² - 60051² = 17165² - 17151² = 8593² - 8565² = 5245² - 5199² = 2657² - 2565² = 907² - 585² = 695² - 51² is the difference of 2 nonnegative squares in 8 ways.
480424 is the sum of 2 positive triangular numbers.
480424 is the difference of 2 positive pentagonal numbers in 5 ways.
480424 = 72² + 218² + 654² is the sum of 3 positive squares.
480424² = 324576² + 354200² is the sum of 2 positive squares in 1 way.
480424² is the sum of 3 positive squares.
480424 is a proper divisor of 461⁶ - 1.
480424 in base 7 = 4040440 and consists of only the digits '0' and '4'.
480424 in base 49 = 444S and consists of only the digits '4' and 'S'.

Number of the day: 8659

Properties of the number 8659:

8659 is a cyclic number.
8659 = 7 × 1237 is semiprime and squarefree.
8659 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 7416 totatives.
8659 has a triangular digit sum 28 in base 10.
8659 = 4330² - 4329² = 622² - 615² is the difference of 2 nonnegative squares in 2 ways.
8659 is the difference of 2 positive pentagonal numbers in 2 ways.
8659 = 1² + 3² + 93² is the sum of 3 positive squares.
8659² = 4284² + 7525² is the sum of 2 positive squares in 1 way.
8659² is the sum of 3 positive squares.
8659 is a proper divisor of 937⁶ - 1.
8659 = '865' + '9' is the concatenation of 2 semiprime numbers.
8659 is an emirpimes in (at least) the following bases: 7, 13, 14, 16, 18, 21, 23, 26, 27, 34, 37, 47, 53, 59, 65, 68, 69, 70, 71, 72, 75, 77, 79, 80, 82, 83, 86, 87, 89, 90, 91, 92, 94, 97, and 98.
8659 is palindromic in (at least) the following bases: 3, 74, and 78.
8659 in base 46 = 44B and consists of only the digits '4' and 'B'.

The number 8659 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A038156: a(n) = n! * Sum_{k=1..n-1} 1/k!.
A060879: Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base.
A069126: Centered 13-gonal numbers.
A082459: Multiply by 1, add 1, multiply by 2, add 2, etc.
A121662: Triangle read by rows: T(i,j) for the recurrence T(i,j)=(T(i-1)+1,j)*i.
A127524: Number of unordered rooted trees where each subtree from given node has the same number of nodes.
A174286: Number of distinct resistances that can be produced using at most n equal resistors in series and/or parallel, confined to the five arms (four arms and the diagonal) of a bridge configuration. Since the bridge requires a minimum of five resistors, the first four terms are zero.
A205768: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors
A247294: Triangle read by rows: T(n,k) is the number of weighted lattice paths B(n) having a total of k uhd and uHd strings.
A247295: Number of weighted lattice paths B(n) having no uhd and no uHd strings.

Number of the day: 61091

Properties of the number 61091:

61091 is a cyclic number.
61091 is the 6153^th prime.
61091 has 9 antidivisors and 61090 totatives.
61091 has an emirp digit sum 17 in base 10.
61091 = 30546² - 30545² is the difference of 2 nonnegative squares in 1 way.
61091 is the difference of 2 positive pentagonal numbers in 1 way.
61091 = 1² + 9² + 247² is the sum of 3 positive squares.
61091² is the sum of 3 positive squares.
61091 is a proper divisor of 1087¹⁴⁹ - 1.
61091 is an emirp in (at least) the following bases: 2, 4, 6, 11, 14, 19, 31, 44, 49, 53, 56, 61, 65, 68, 72, 74, 77, 79, 82, 89, 90, and 92.
61091 is palindromic in (at least) base 95.

The number 61091 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A153402: Smaller of 3 consecutive prime numbers such that p1*p2*p3+d1+d2-1=average of twin prime pairs, d1(delta)=p2-p1,d2(delta)=p3-p2.
A337251: Positive integers k such that k^2 = A^2+B^2+C^2 and A^3+B^3+C^3 = m^3, where gcd(A,B,C) = 1 and A, B, C, m are positive integers.

Number of the day: 334

Properties of the number 334:

334 = 2 × 167 is semiprime and squarefree.
334 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 166 totatives.
334 has a semiprime digit sum 10 in base 10.
334 has a triangular digit sum 10 in base 10.
334 has a triangular digit product 36 in base 10.
Reversing the decimal digits of 334 results in a prime.
334 is the difference of 2 positive pentagonal numbers in 2 ways.
334 = 3² + 10² + 15² is the sum of 3 positive squares.
334² is the sum of 3 positive squares.
334 is a proper divisor of 1669² - 1.
334 = '33' + '4' is the concatenation of 2 semiprime numbers.
334 = '3' + '34' is the concatenation of 2 Fibonacci numbers.
334 is an emirpimes in (at least) the following bases: 3, 5, 9, 12, 13, 14, 15, 16, 17, 18, 19, 29, 32, 33, 34, 35, 37, 39, 41, 42, 45, 46, 49, 50, 55, 56, 57, 59, 60, 61, 63, 64, 67, 69, 71, 75, 84, 85, 86, 91, 92, 94, 97, and 100.
334 is palindromic in (at least) the following bases: -8, -10, and -37.
334 in base 3 = 110101 and consists of only the digits '0' and '1'.
334 in base 7 = 655 and consists of only the digits '5' and '6'.
334 in base 9 = 411 and consists of only the digits '1' and '4'.
334 consists of only the digits '3' and '4'.

The number 334 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000068: Numbers n such that n^4 + 1 is prime.
A003052: Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).
A003278: Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k.
A005237: Numbers n such that n and n+1 have the same number of divisors.
A005836: Numbers n whose base 3 representation contains no 2.
A100484: Even semiprimes.
A108917: Number of knapsack partitions of n.
A161344: Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
A191113: Increasing sequence generated by these rules:a(1)=1, and if x is in a then 3x-2 and 4x-2 are in a.
A210000: Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n}.

Number of the day: 456564

Properties of the number 456564:

456564 = 2² × 3 × 38047 is the 418358^th composite number and is not squarefree.
456564 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 152184 totatives.
456564 has a sphenic digit sum 30 in base 10.
456564 has an oblong digit sum 30 in base 10.
456564 = 114142² - 114140² = 38050² - 38044² is the difference of 2 nonnegative squares in 2 ways.
456564 is the sum of 2 positive triangular numbers.
456564 is the difference of 2 positive pentagonal numbers in 1 way.
456564 = 28² + 122² + 664² is the sum of 3 positive squares.
456564² is the sum of 3 positive squares.
456564 is a proper divisor of 1231³⁴ - 1.

Number of the day: 92687

Ernst Leonard Lindelöf was born on this day 151 years ago.

Properties of the number 92687:

92687 is a cyclic number.
92687 = 7 × 13241 is semiprime and squarefree.
92687 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 79440 totatives.
Reversing the decimal digits of 92687 results in an emirpimes.
92687 = (108 × 109)/2 + … + (121 × 122)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
92687 = 46344² - 46343² = 6624² - 6617² is the difference of 2 nonnegative squares in 2 ways.
92687 is the difference of 2 positive pentagonal numbers in 2 ways.
92687 is not the sum of 3 positive squares.
92687² = 6440² + 92463² is the sum of 2 positive squares in 1 way.
92687² is the sum of 3 positive squares.
92687 is a proper divisor of 1471³³¹ - 1.
92687 = '926' + '87' is the concatenation of 2 semiprime numbers.
92687 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 6, 10, 15, 16, 18, 19, 23, 26, 31, 32, 35, 37, 39, 40, 44, 45, 51, 52, 54, 56, 59, 61, 69, 71, 81, 82, 84, 85, 87, 90, 91, and 98.
92687 is palindromic in (at least) the following bases: 46, 50, and -69.
92687 in base 46 = hah and consists of only the digits 'a' and 'h'.
92687 in base 50 = b3b and consists of only the digits '3' and 'b'.

Number of the day: 1993563

Cesare Arzelà was born on this day 174 years ago.

Properties of the number 1993563:

1993563 = 3² × 11 × 13 × 1549 is the 1845087^th composite number and is not squarefree.
1993563 has 4 distinct prime factors, 24 divisors, 43 antidivisors and 1114560 totatives.
1993563 has a triangular digit sum 36 in base 10.
1993563 is the difference of 2 nonnegative squares in 12 ways.
1993563 is the difference of 2 positive pentagonal numbers in 3 ways.
1993563 = 31² + 41² + 1411² is the sum of 3 positive squares.
1993563² = 766755² + 1840212² = 446688² + 1942875² = 1050885² + 1694088² = 1159587² + 1621620² is the sum of 2 positive squares in 4 ways.
1993563² is the sum of 3 positive squares.
1993563 is a proper divisor of 1637²⁰ - 1.
1993563 = '19' + '93563' is the concatenation of 2 prime numbers.

Number of the day: 5992794074

Properties of the number 5992794074:

5992794074 = 2 × 2996397037 is semiprime and squarefree.
5992794074 has 2 distinct prime factors, 4 divisors, 69 antidivisors and 2996397036 totatives.
5992794074 has an oblong digit sum 56 in base 10.
5992794074 is the sum of 2 positive triangular numbers.
5992794074 = 11293² + 76585² is the sum of 2 positive squares in 1 way.
5992794074 = 63² + 572² + 77411² is the sum of 3 positive squares.
5992794074² = 1729748810² + 5737730376² is the sum of 2 positive squares in 1 way.
5992794074² is the sum of 3 positive squares.
5992794074 is a proper divisor of 967^1290438 - 1.
5992794074 is an emirpimes in (at least) the following bases: 2, 4, 32, 36, 40, 42, 46, 48, 50, 54, 60, 64, 71, 77, 86, 91, 92, and 100.

Number of the day: 40401

Properties of the number 40401:

40401 = 3² × 67² is the 36164^th composite number and is not squarefree.
40401 has 2 distinct prime factors, 9 divisors, 18 antidivisors and 26532 totatives.
40401 = 201² is a perfect power of a semiprime.
40401 has a semiprime digit sum 9 in base 10.
40401 = 201² is a perfect square.
40401 = (200 × 201)/2 + (201 × 202)/2 is the sum of at least 2 consecutive triangular numbers in 1 way. In fact, it is the sum of 2 triangular numbers.
40401 = 20201² - 20200² = 6735² - 6732² = 2249² - 2240² = 335² - 268² = 201² - 0² is the difference of 2 nonnegative squares in 5 ways.
40401 is the difference of 2 positive pentagonal numbers in 1 way.
40401 is the sum of 3 positive squares.
40401² is the sum of 3 positive squares.
40401 is a proper divisor of 1471³³ - 1.
40401 is palindromic in (at least) the following bases: 66, -53, and -68.

The number 40401 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A017042: a(n) = (7*n + 5)^2.
A019544: Squares whose digits are squares.
A035090: Non-palindromic squares which when written backwards remain square (and still have the same number of digits).
A036896: Odd refactorable numbers.
A061457: Numbers n such that n and its reversal are both squares.
A062917: Nonpalindromic numbers n such that n is not divisible by 10 and n*R(n) is a square, where R(n) is the reversal of n (A004086).
A184095: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with rows and columns in nondecreasing order and with no 2X2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one
A202835: E.g.f.: exp(9*x/(1-2*x)) / sqrt(1-4*x^2).
A225873: Squares that become prime when their most significant (or leftmost) digit is removed.
A277948: Squares whose largest decimal digit is 4.

Number of the day: 200311

Georg Cantor was born on this day 176 years ago.

Paul Richard Halmos was born on this day 105 years ago.

Properties of the number 200311:

200311 is a cyclic number.
200311 = 17 × 11783 is semiprime and squarefree.
200311 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 188512 totatives.
200311 has a prime digit sum 7 in base 10.
Reversing the decimal digits of 200311 results in an emirpimes.
200311 = 100156² - 100155² = 5900² - 5883² is the difference of 2 nonnegative squares in 2 ways.
200311 is the difference of 2 positive pentagonal numbers in 2 ways.
200311 is not the sum of 3 positive squares.
200311² = 94264² + 176745² is the sum of 2 positive squares in 1 way.
200311² is the sum of 3 positive squares.
200311 is a proper divisor of 1361¹³⁷ - 1.
200311 = '2003' + '11' is the concatenation of 2 prime numbers.
200311 is an emirpimes in (at least) the following bases: 2, 5, 10, 13, 15, 18, 19, 20, 23, 25, 26, 31, 32, 34, 35, 43, 44, 45, 47, 50, 51, 52, 54, 56, 58, 60, 63, 66, 68, 72, 77, 80, 81, 85, 86, 87, 92, 93, and 97.
200311 is palindromic in (at least) the following bases: -70, and -77.

Number of the day: 2518547605

Properties of the number 2518547605:

2518547605 = 5 × 7 × 241 × 298583 is the 2396246842^th composite number and is squarefree.
2518547605 has 4 distinct prime factors, 16 divisors, 35 antidivisors and 1719832320 totatives.
2518547605 has a prime digit sum 43 in base 10.
2518547605 = 1259273803² - 1259273802² = 251854763² - 251854758² = 179896261² - 179896254² = 35979269² - 35979234² = 5225323² - 5225082² = 1045643² - 1044438² = 747301² - 745614² = 153509² - 145074² is the difference of 2 nonnegative squares in 8 ways.
2518547605 is the sum of 2 positive triangular numbers.
2518547605 is the difference of 2 positive pentagonal numbers in 8 ways.
2518547605 = 185² + 282² + 50184² is the sum of 3 positive squares.
2518547605² = 1511128563² + 2014838084² = 994878556² + 2313719667² = 307241907² + 2499736876² = 1254048600² + 2184134645² is the sum of 2 positive squares in 4 ways.
2518547605² is the sum of 3 positive squares.
2518547605 is a proper divisor of 3⁵³¹⁶⁰ - 1.