Number of the day: 6423991668601

Properties of the number 6423991668601:

6423991668601 = 13 × 97 × 9967 × 511123 is composite and squarefree.
6423991668601 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 5868105813504 totatives.
6423991668601 has a prime digit sum 61 in base 10.
Reversing the decimal digits of 6423991668601 results in a sphenic number.
6423991668601 = 3211995834301² - 3211995834300² = 247076602645² - 247076602632² = 33113359165² - 33113359068² = 2547182101² - 2547180840² = 322268035² - 322258068² = 24854251² - 24724680² = 6539755² - 6028632² = 3805699² - 2838900² is the difference of 2 nonnegative squares in 8 ways.
6423991668601 is the difference of 2 positive pentagonal numbers in 8 ways.
6423991668601 = 360² + 22451² + 2534460² is the sum of 3 positive squares.
6423991668601² = 4304736685145² + 4768323712776² = 2139632435220² + 6057197536849² = 2745861625199² + 5807573752740² = 2470766026385² + 5929838463324² is the sum of 2 positive squares in 4 ways.
6423991668601² is the sum of 3 positive squares.
6423991668601 is a divisor of 457^8177952 - 1.

Number of the day: 772627975

Properties of the number 772627975:

772627975 = 5² × 7 × 449 × 9833 is the 732818373^th composite number and is not squarefree.
772627975 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 528568320 totatives.
772627975 is the difference of 2 nonnegative squares in 12 ways.
772627975 is the sum of 2 positive triangular numbers.
772627975 is the difference of 2 positive pentagonal numbers in 12 ways.
772627975 is not the sum of 3 positive squares.
772627975² = 481817000² + 603992025² = 23058385² + 772283820² = 194103420² + 747848815² = 444923584² + 631662087² = 293426553² + 714741104² = 377727140² + 674000145² = 102218375² + 765836400² = 312563832² + 706581799² = 541276540² + 551338095² = 116304552² + 763824089² = 405220305² + 657837740² = 70526400² + 769402375² = 283138009² + 718878888² = 518062545² + 573206060² = 147727321² + 758373672² = 534938600² + 557489625² = 93457105² + 766954860² = 125028540² + 762444655² = 385407232² + 669638151² = 357443961² + 684972848² = 463576785² + 618102380² = 216335833² + 741722856² is the sum of 2 positive squares in 22 ways.
772627975² is the sum of 3 positive squares.
772627975 is a divisor of 349¹⁹⁶⁶⁴ - 1.

Number of the day: 94640

Properties of the number 94640:

94640 = 2⁴ × 5 × 7 × 13² is the 85512^th composite number and is not squarefree.
94640 has 4 distinct prime factors, 60 divisors, 17 antidivisors and 29952 totatives.
94640 has a prime digit sum 23 in base 10.
94640 is the difference of 2 nonnegative squares in 18 ways.
94640 is the difference of 2 positive pentagonal numbers in 5 ways.
94640 = 60² + 76² + 292² is the sum of 3 positive squares.
94640² = 36400² + 87360² = 23296² + 91728² = 48048² + 81536² = 56784² + 75712² = 66640² + 67200² = 12992² + 93744² = 13776² + 93632² is the sum of 2 positive squares in 7 ways.
94640² is the sum of 3 positive squares.
94640 is a divisor of 239⁴ - 1.
94640 is palindromic in (at least) base 54.
94640 in base 52 = Z00 and consists of only the digits '0' and 'Z'.
94640 in base 54 = WOW and consists of only the digits 'O' and 'W'.

The number 94640 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.
A089660: Let S1 := (n,t)->add( k^t * add( binomial(n,j), j=0..k), k=0..n); a(n) = S1(n,3).
A172373: A beta integer combination triangle of a Narayana type: a=1:f(n, a) = a*f(n - 1, a) + a*f(n - 2, a);c(n,a)=If[n == 0, 1, Product[f(i, a), {i, 1, n}]];w(n,m,q)=c(n - 1, q)*c(n, q)/(c(m - 1, q)*c(n - m, q)*c(m - 1, q)*c(n - m + 1, q)*f(m, q))
A210373: Number of 2 X 2 matrices with all elements in {0,1,...,n} and positive odd determinant.
A230361: Integer areas of the tangential triangles corresponding to the integer-sided triangles with integer areas.
A249708: Number of length 2+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms

Number of the day: 12229

Properties of the number 12229:

12229 = 7 × 1747 is semiprime and squarefree.
12229 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 10476 totatives.
12229 has an oblong digit product 72 in base 10.
Reversing the decimal digits of 12229 results in a prime.
12229 = 6115² - 6114² = 877² - 870² is the difference of 2 nonnegative squares in 2 ways.
12229 is the difference of 2 positive pentagonal numbers in 2 ways.
12229 = 23² + 60² + 90² is the sum of 3 positive squares.
12229² is the sum of 3 positive squares.
12229 is a divisor of 547⁹ - 1.
12229 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 11, 16, 17, 19, 24, 25, 27, 29, 31, 35, 38, 39, 41, 43, 46, 53, 58, 59, 67, 71, 72, 73, 75, 80, 82, 86, 87, 93, 94, and 97.
12229 is palindromic in (at least) base -42.
12229 in base 41 = 7BB and consists of only the digits '7' and 'B'.

The number 12229 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A016849: Expansion of 1/((1-3x)(1-4x)(1-8x)).
A031846: Period of continued fraction for sqrt(n) contains exactly 78 ones.
A058829: Numbers n such that 6^n - n is prime.
A114958: a(n) = 6*2^(n+1) - 5*(n+1) - 4.
A126094: Numbers k such that prime(k) = A123206(n).
A150909: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, -1), (1, 0, -1), (1, 0, 1), (1, 1, 1)}
A152233: Similar to A072921 but starting with 4.
A182307: a(n+1) = a(n) + floor(a(n)/6) with a(0)=6.
A237821: Number of partitions of n such that 2*(least part) <= greatest part.
A245402: Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.

Number of the day: 175742

Properties of the number 175742:

175742 = 2 × 7 × 12553 is a sphenic number and squarefree.
175742 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 75312 totatives.
175742 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 175742 results in a semiprime.
175742 = 9² + 10² + 419² is the sum of 3 positive squares.
175742² = 9408² + 175490² is the sum of 2 positive squares in 1 way.
175742² is the sum of 3 positive squares.
175742 is a divisor of 1303⁵²³ - 1.
175742 is palindromic in (at least) the following bases: 76, 91, 99, and -43.

The number 175742 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A071810: Number of subsets of the first n primes whose sum is a prime.

Number of the day: 237902

Properties of the number 237902:

237902 = 2 × 7 × 16993 is a sphenic number and squarefree.
237902 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 101952 totatives.
237902 has a prime digit sum 23 in base 10.
237902 = 2² + 27² + 487² is the sum of 3 positive squares.
237902² = 88690² + 220752² is the sum of 2 positive squares in 1 way.
237902² is the sum of 3 positive squares.
237902 is a divisor of 769³⁶ - 1.
237902 is palindromic in (at least) the following bases: 67, and 91.

Number of the day: 8308549141

Joseph-Louis Lagrange was born on this day 281 years ago.

Properties of the number 8308549141:

8308549141 = 23 × 601 × 601067 is a sphenic number and squarefree.
8308549141 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 7934071200 totatives.
8308549141 has a prime digit sum 43 in base 10.
8308549141 = 4154274571² - 4154274570² = 180620645² - 180620622² = 6912571² - 6911970² = 307445² - 293622² is the difference of 2 nonnegative squares in 4 ways.
8308549141 is the sum of 2 positive triangular numbers.
8308549141 is the difference of 2 positive pentagonal numbers in 4 ways.
8308549141 = 1921² + 4116² + 91038² is the sum of 3 positive squares.
8308549141² = 3317889840² + 7617322091² is the sum of 2 positive squares in 1 way.
8308549141² is the sum of 3 positive squares.
8308549141 is a divisor of 691^6010660 - 1.
8308549141 = '83085491' + '41' is the concatenation of 2 prime numbers.
8308549141 = '8308549' + '141' is the concatenation of 2 semiprime numbers.

Number of the day: 482369954545

Properties of the number 482369954545:

482369954545 = 5 × 96473990909 is semiprime and squarefree.
482369954545 has 2 distinct prime factors, 4 divisors, 47 antidivisors and 385895963632 totatives.
482369954545 = 241184977273² - 241184977272² = 48236995457² - 48236995452² is the difference of 2 nonnegative squares in 2 ways.
482369954545 is the difference of 2 positive pentagonal numbers in 2 ways.
482369954545 = 475047² + 506656² = 76044² + 690353² is the sum of 2 positive squares in 2 ways.
482369954545 = 4410² + 5347² + 694494² is the sum of 3 positive squares.
482369954545² = 289421972727² + 385895963636² = 104994407064² + 470804574673² = 31030650127² + 481370825664² = 313647015500² + 366478270455² is the sum of 2 positive squares in 4 ways.
482369954545² is the sum of 3 positive squares.
482369954545 is a divisor of 71^24118497727 - 1.
482369954545 = '482369' + '954545' is the concatenation of 2 semiprime numbers.
482369954545 is an emirpimes in (at least) the following bases: 5, 17, 20, 25, 44, 45, 47, 55, 64, 86, 87, 92, 95, and 98.

Number of the day: 7187

David Hilbert was born on this day 155 years ago.

Properties of the number 7187:

7187 is the 918^th prime.
7187 has 13 antidivisors and 7186 totatives.
7187 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 7187 results in an emirp.
7187 = 3594² - 3593² is the difference of 2 nonnegative squares in 1 way.
7187 is the difference of 2 positive pentagonal numbers in 1 way.
7187 = 3² + 17² + 83² is the sum of 3 positive squares.
7187² is the sum of 3 positive squares.
7187 is a divisor of 3³⁵⁹³ - 1.
7187 is an emirp in (at least) the following bases: 9, 10, 11, 19, 21, 23, 28, 29, 32, 36, 37, 39, 41, 46, 47, 55, 57, 59, 60, 61, 63, 64, 69, 71, 76, 77, 80, 85, 86, 88, 89, 97, and 98.
7187 is palindromic in (at least) the following bases: 6, -22, -25, -26, -38, and -42.
7187 in base 5 = 212222 and consists of only the digits '1' and '2'.
7187 in base 11 = 5444 and consists of only the digits '4' and '5'.
7187 in base 23 = ddb and consists of only the digits 'b' and 'd'.
7187 in base 24 = cbb and consists of only the digits 'b' and 'c'.
7187 in base 25 = bcc and consists of only the digits 'b' and 'c'.
7187 in base 37 = 599 and consists of only the digits '5' and '9'.

The number 7187 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A029974: Primes that are palindromic in base 6.
A045713: Primes with first digit 7.
A059940: Smallest prime p such that x = n is a solution mod p of x^3 = 2, or 0 if no such prime exists.
A060315: a(1)=1; a(n) is the smallest positive integer that cannot be obtained from the integers {0, 1, ..., n-1} using each number at most once and the operators +, -, *, /.
A085318: Primes which are the sum of three positive 4th powers.
A126657: Prime numbers that are the sum of three distinct positive fourth powers.
A127340: Primes that are the sum of 11 consecutive primes.
A153116: Primes p such that p^2 +- 12 are also primes.
A153209: Primes of the form 2*p+1 where p is prime and p+1 is squarefree.
A198164: Primes from merging of 4 successive digits in decimal expansion of sqrt(2).

Number of the day: 5694786632

Properties of the number 5694786632:

5694786632 = 2³ × 139 × 5121211 is the 5428812002^th composite number and is not squarefree.
5694786632 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 2826907920 totatives.
5694786632 has an oblong digit sum 56 in base 10.
5694786632 = 1423696659² - 1423696657² = 711848331² - 711848327² = 10242561² - 10242283² = 5121489² - 5120933² is the difference of 2 nonnegative squares in 4 ways.
5694786632 is the sum of 2 positive triangular numbers.
5694786632 = 558² + 752² + 75458² is the sum of 3 positive squares.
5694786632² is the sum of 3 positive squares.
5694786632 is a divisor of 1669³⁴¹⁴¹⁴ - 1.

Number of the day: 574

Properties of the number 574:

574 = 2 × 7 × 41 is a sphenic number and squarefree.
574 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 240 totatives.
574 is the sum of 2 positive triangular numbers.
574 is the difference of 2 positive pentagonal numbers in 3 ways.
574 = 5² + 15² + 18² is the sum of 3 positive squares.
574² = 126² + 560² is the sum of 2 positive squares in 1 way.
574² is the sum of 3 positive squares.
574 is a divisor of 83² - 1.
574 = '57' + '4' is the concatenation of 2 semiprime numbers.
574 is palindromic in (at least) the following bases: 9, 40, 81, -3, -9, and -22.
574 in base 5 = 4244 and consists of only the digits '2' and '4'.
574 in base 9 = 707 and consists of only the digits '0' and '7'.
574 in base 23 = 11m and consists of only the digits '1' and 'm'.

The number 574 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002865: Number of partitions of n that do not contain 1 as a part.
A008865: a(n) = n^2 - 2.
A014616: a(n) = solution to the postage stamp problem with 2 denominations and n stamps.
A049450: Pentagonal numbers multiplied by 2: n*(3*n-1).
A144064: Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is Euler transform of (j->k).
A187219: Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1.
A194368: Numbers n such that Sum_{k=1..n} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part.
A210000: Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n}.
A235227: Numbers whose sum of digits is 16.
A259934: Infinite sequence starting with a(0)=0 such that A049820(a(k)) = a(k-1) for all k>=1, where A049820(n) = n - (number of divisors of n).

Number of the day: 8815

Properties of the number 8815:

8815 = 5 × 41 × 43 is a sphenic number and squarefree.
8815 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 6720 totatives.
8815 has a semiprime digit sum 22 in base 10.
8815 = 4408² - 4407² = 884² - 879² = 128² - 87² = 124² - 81² is the difference of 2 nonnegative squares in 4 ways.
8815 is the sum of 2 positive triangular numbers.
8815 is the difference of 2 positive pentagonal numbers in 3 ways.
8815 is not the sum of 3 positive squares.
8815² = 3612² + 8041² = 1935² + 8600² = 5719² + 6708² = 5289² + 7052² is the sum of 2 positive squares in 4 ways.
8815² is the sum of 3 positive squares.
8815 is a divisor of 1721² - 1.
8815 = '881' + '5' is the concatenation of 2 prime numbers.
8815 is palindromic in (at least) the following bases: 78, -25, and -27.
8815 in base 24 = f77 and consists of only the digits '7' and 'f'.
8815 in base 26 = d11 and consists of only the digits '1' and 'd'.

The number 8815 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067701: Numbers n such that phi(n-1) + phi(n+1) = phi(2n).
A067724: a(n) = 5*n^2 + 10*n.
A085249: Terms x of A002977 such that both (x-1)/2 and (x-1)/3 are also terms of A002977.
A160794: Vertex number of a rectangular spiral related to Fibonacci numbers and prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the Fibonacci numbers, while the distances between nearest edges perpendicular to the initial edge are the prime numbers.
A172193: 5*n^2+31*n+1.
A177342: a(n) = (4*n^3-3*n^2+5*n-3)/3.
A191313: Sum of the abscissae of the first returns to the horizontal axis (assumed to be 0 if there are no such returns) in all dispersed Dyck paths of length n (i.e. Motzkin paths of length n with no (1,0) steps at positive heights).
A191834: Numbers n not divisible by 2 or 3 such that k^k == k+1 (mod n) has no nonzero solutions.
A225274: Number of distinct values of the sum of i^2 over 7 realizations of i in 0..n
A255401: Numbers n with the property that its k-th smallest divisor, for all 1 <= k <= tau(n), contains exactly k "1" digits in its binary representation.

Number of the day: 349950494

Properties of the number 349950494:

349950494 = 2 × 739 × 236773 is a sphenic number and squarefree.
349950494 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 174737736 totatives.
349950494 has a prime digit sum 47 in base 10.
349950494 = 142² + 527² + 18699² is the sum of 3 positive squares.
349950494² = 204266990² + 284148456² is the sum of 2 positive squares in 1 way.
349950494² is the sum of 3 positive squares.
349950494 is a divisor of 317⁵⁹¹⁹³ - 1.
349950494 = '34' + '9950494' is the concatenation of 2 semiprime numbers.

Number of the day: 947030

Properties of the number 947030:

947030 = 2 × 5 × 7 × 83 × 163 is the 872329^th composite number and is squarefree.
947030 has 5 distinct prime factors, 32 divisors, 31 antidivisors and 318816 totatives.
947030 has a prime digit sum 23 in base 10.
947030 is the difference of 2 positive pentagonal numbers in 7 ways.
947030 = 62² + 65² + 969² is the sum of 3 positive squares.
947030² = 568218² + 757624² is the sum of 2 positive squares in 1 way.
947030² is the sum of 3 positive squares.
947030 is a divisor of 1327³⁶ - 1.
947030 = '9470' + '30' is the concatenation of 2 sphenic numbers.

Number of the day: 706249

Properties of the number 706249:

706249 = 19 × 37171 is semiprime and squarefree.
706249 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 669060 totatives.
706249 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 706249 results in a prime.
706249 = 15² + … + 128² is the sum of at least 2 consecutive positive squares in 1 way.
706249 = 353125² - 353124² = 18595² - 18576² is the difference of 2 nonnegative squares in 2 ways.
706249 is the sum of 2 positive triangular numbers.
706249 is the difference of 2 positive pentagonal numbers in 2 ways.
706249 = 28² + 243² + 804² is the sum of 3 positive squares.
706249² is the sum of 3 positive squares.
706249 is a divisor of 241⁹⁰ - 1.
706249 = '706' + '249' is the concatenation of 2 semiprime numbers.
706249 is an emirpimes in (at least) the following bases: 2, 3, 5, 9, 11, 12, 13, 17, 21, 24, 26, 30, 32, 35, 36, 37, 39, 52, 53, 55, 58, 63, 69, 70, 71, 73, 82, 83, 84, 87, 90, 92, 95, 97, and 98.

Number of the day: 656292204869201

Properties of the number 656292204869201:

656292204869201 is prime.
656292204869201 has 5 antidivisors and 656292204869200 totatives.
656292204869201 has an emirpimes digit sum 62 in base 10.
656292204869201 = 328146102434601² - 328146102434600² is the difference of 2 nonnegative squares in 1 way.
656292204869201 is the difference of 2 positive pentagonal numbers in 1 way.
656292204869201 = 12510455² + 22355776² is the sum of 2 positive squares in 1 way.
656292204869201 = 17540² + 27399² + 25618180² is the sum of 3 positive squares.
656292204869201² = 343269236255151² + 559361859276160² is the sum of 2 positive squares in 1 way.
656292204869201² is the sum of 3 positive squares.
656292204869201 is a divisor of 1621^{1640730512173} - 1.
656292204869201 = '65629' + '2204869201' is the concatenation of 2 prime numbers.
656292204869201 = '65' + '6292204869201' is the concatenation of 2 semiprime numbers.
656292204869201 is an emirp in (at least) the following bases: 2, 13, 61, 75, 79, and 99.

Number of the day: 12962

Sofia Kovalevskaya was born on this day 167 years ago.

Properties of the number 12962:

12962 = 2 × 6481 is semiprime and squarefree.
12962 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 6480 totatives.
12962 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 12962 results in a prime.
12962 = 71² + 89² is the sum of 2 positive squares in 1 way.
12962 = 7² + 12² + 113² is the sum of 3 positive squares.
12962² = 2880² + 12638² is the sum of 2 positive squares in 1 way.
12962² is the sum of 3 positive squares.
12962 is a divisor of 601¹⁰ - 1.
12962 = '129' + '62' is the concatenation of 2 emirpimes.
12962 is an emirpimes in (at least) the following bases: 2, 6, 8, 13, 18, 23, 27, 29, 30, 31, 36, 41, 42, 43, 47, 50, 51, 55, 58, 60, 61, 62, 66, 71, 77, 78, 82, 85, 86, 87, 88, 95, 96, and 98.
12962 is palindromic in (at least) the following bases: 72, 80, -62, -81, -90, and -96.

The number 12962 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005901: Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice.
A010022: a(0) = 1, a(n) = 40*n^2 + 2 for n>0.
A099792: Positions of records for terms in the continued fraction of the Glaisher-Kinkelin constant A.
A107317: Semiprimes of the form 2*(m^2 + m + 1) (implying that m^2 + m + 1 is a prime).
A139485: a(1)=1. For m>=0 and 1<=k<=2^m, a(2^m +k) = a(k) + sum{j=1 to 2^m) a(j).
A212074: Beach-Williams Pell numbers of type 2p (p prime).
A213359: Sum of all parts that are not the smallest part (counted with multiplicity) of all partitions of n.
A230831: T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero
A238728: Number of standard Young tableaux with n cells where the largest value n is contained in the last row.
A239729: Number of partitions p of n such that if h = min(p), then h is an (h,2)-separator of p; see Comments.

Number of the day: 184127285037141

Alfred Tarski was born on this day 116 years ago.

Properties of the number 184127285037141:

184127285037141 = 3² × 137 × 149332753477 is composite and not squarefree.
184127285037141 has 3 distinct prime factors, 12 divisors, 35 antidivisors and 121855526836416 totatives.
184127285037141 = 92063642518571² - 92063642518570² = 30687880839525² - 30687880839522² = 10229293613179² - 10229293613170² = 671997390715² - 671997390578² = 223999130421² - 223999130010² = 74666377355² - 74666376122² is the difference of 2 nonnegative squares in 6 ways.
184127285037141 is the difference of 2 positive pentagonal numbers in 2 ways.
184127285037141 = 5180946² + 12541335² = 4084950² + 12939879² is the sum of 2 positive squares in 2 ways.
184127285037141 = 7490² + 15521² + 13569340² is the sum of 3 positive squares.
184127285037141² = 129951958805820² + 130442882127309² = 118271540753784² + 141119452035765² = 105717517442100² + 150753652032141² = 15810087937284² + 183447262761165² is the sum of 2 positive squares in 4 ways.
184127285037141² is the sum of 3 positive squares.
184127285037141 is a divisor of 547^2164242804 - 1.
184127285037141 = '1841' + '27285037141' is the concatenation of 2 semiprime numbers.

Number of the day: 23434639

Properties of the number 23434639:

23434639 = 29 × 53 × 79 × 193 is the 21960788^th composite number and is squarefree.
23434639 has 4 distinct prime factors, 16 divisors, 31 antidivisors and 21805056 totatives.
23434639 has a semiprime digit sum 34 in base 10.
23434639 has a Fibonacci digit sum 34 in base 10.
23434639 = 11717320² - 11717319² = 404060² - 404031² = 221108² - 221055² = 148360² - 148281² = 60808² - 60615² = 8392² - 6855² = 6260² - 3969² = 4892² - 705² is the difference of 2 nonnegative squares in 8 ways.
23434639 is the difference of 2 positive pentagonal numbers in 6 ways.
23434639 is not the sum of 3 positive squares.
23434639² = 11535185² + 20399064² = 11225900² + 20570889² = 982839² + 23414020² = 15435889² + 17632800² = 6816436² + 22421385² = 6057720² + 22638161² = 16277160² + 16859311² = 5715255² + 22727036² = 7154161² + 22315920² = 16161820² + 16969911² = 5870095² + 22687536² = 4757064² + 22946735² = 12380564² + 19897335² is the sum of 2 positive squares in 13 ways.
23434639² is the sum of 3 positive squares.
23434639 is a divisor of 853¹⁵⁶ - 1.
23434639 = '2343463' + '9' is the concatenation of 2 semiprime numbers.

Number of the day: 975761

Properties of the number 975761:

975761 = 101 × 9661 is semiprime and squarefree.
975761 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 966000 totatives.
975761 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 975761 results in an emirpimes.
975761 = 487881² - 487880² = 4881² - 4780² is the difference of 2 nonnegative squares in 2 ways.
975761 is the difference of 2 positive pentagonal numbers in 2 ways.
975761 = 631² + 760² = 620² + 769² is the sum of 2 positive squares in 2 ways.
975761 = 51² + 94² + 982² is the sum of 3 positive squares.
975761² = 193220² + 956439² = 179439² + 959120² = 206961² + 953560² = 14039² + 975660² is the sum of 2 positive squares in 4 ways.
975761² is the sum of 3 positive squares.
975761 is a divisor of 139¹⁰⁰ - 1.
975761 is an emirpimes in (at least) the following bases: 2, 4, 7, 8, 9, 10, 17, 22, 23, 27, 38, 39, 41, 52, 55, 56, 59, 65, 71, 73, 78, 82, 83, 84, 85, 90, 92, 93, 95, 96, and 98.

Number of the day: 3742

Properties of the number 3742:

3742 = 2 × 1871 is semiprime and squarefree.
3742 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 1870 totatives.
Reversing the decimal digits of 3742 results in a prime.
3742 is the sum of 2 positive triangular numbers.
3742 is the difference of 2 positive pentagonal numbers in 2 ways.
3742 = 14² + 39² + 45² is the sum of 3 positive squares.
3742² is the sum of 3 positive squares.
3742 is a divisor of 191⁵ - 1.
3742 is an emirpimes in (at least) the following bases: 2, 4, 5, 7, 8, 12, 13, 17, 18, 20, 21, 32, 34, 37, 41, 43, 44, 46, 47, 49, 50, 54, 60, 65, 71, 72, 73, 74, 76, 80, 82, 83, 85, 86, 89, 91, 94, 95, 99, and 100.
3742 is palindromic in (at least) the following bases: 16, -44, -55, and -87.
3742 in base 16 = e9e and consists of only the digits '9' and 'e'.
3742 in base 30 = 44m and consists of only the digits '4' and 'm'.
3742 in base 43 = 211 and consists of only the digits '1' and '2'.

The number 3742 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002703: Sets with a congruence property.
A079222: Triangle T(n,d) (listed row-wise: T(1,1)=1, T(2,1)=1, T(2,2)=1, T(3,1)=2, T(3,2)=2, T(3,3)=1, ...) giving the number of n-edge general plane trees with root degree d that are fixed by the six-fold application of Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees).
A080855: (9*n^2-3*n+2)/2.
A084849: a(n) = 1 + n + 2*n^2.
A125264: Numbers n such that n^10 + 9 is prime.
A185264: Number of disconnected 6-regular simple graphs on n vertices with girth at least 4.
A189912: Extended Motzkin numbers, Sum{k>=0} C(n,k)C(k), C(k) the extended Catalan number A057977(k).
A214203: Number of rooted planar binary unlabeled trees with n leaves and caterpillar index <= 5.
A243366: Number T(n,k) of Dyck paths of semilength n having exactly k (possibly overlapping) occurrences of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)); triangle T(n,k), n>=0, k<=0<=max(0,floor(n/2)-1), read by rows.
A249508: Lengths of complete iterations (direct and reverse branches) of the Oldenburger-Kolakoski sequence A000002.

Number of the day: 53952

Properties of the number 53952:

53952 = 2⁶ × 3 × 281 is the 48454^th composite number and is not squarefree.
53952 has 3 distinct prime factors, 28 divisors, 9 antidivisors and 17920 totatives.
53952 is the difference of 2 nonnegative squares in 10 ways.
53952 = 56² + 104² + 200² is the sum of 3 positive squares.
53952² = 30720² + 44352² is the sum of 2 positive squares in 1 way.
53952² is the sum of 3 positive squares.
53952 is a divisor of 89⁸ - 1.
53952 is palindromic in (at least) base -43.
53952 in base 3 = 2202000020 and consists of only the digits '0' and '2'.
53952 in base 42 = UOO and consists of only the digits 'O' and 'U'.

The number 53952 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A080877: a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=2.
A080878: a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=3.
A098648: Expansion of (1-3*x)/(1 - 6*x + 4*x^2).
A149377: 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, 0), (-1, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}
A205071: Number of (n+1)X8 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock differing from the number in all its horizontal and vertical neighbors
A234645: Sum of the divisors of n^3+1.

Number of the day: 951553

Properties of the number 951553:

951553 is the 75024^th prime.
951553 has 9 antidivisors and 951552 totatives.
951553 has a triangular digit sum 28 in base 10.
951553 has sum of divisors equal to 951554 which is semiprime.
Reversing the decimal digits of 951553 results in a sphenic number.
951553 = 475777² - 475776² is the difference of 2 nonnegative squares in 1 way.
951553 is the difference of 2 positive pentagonal numbers in 1 way.
951553 = 548² + 807² is the sum of 2 positive squares in 1 way.
951553 = 21² + 134² + 966² is the sum of 3 positive squares.
951553² = 350945² + 884472² is the sum of 2 positive squares in 1 way.
951553² is the sum of 3 positive squares.
951553 is a divisor of 1399²¹ - 1.
951553 = '9' + '51553' is the concatenation of 2 semiprime numbers.
951553 is an emirp in (at least) the following bases: 2, 19, 21, 27, 29, 35, 37, 56, 57, 61, 64, 68, 69, 75, 79, 83, 84, 85, 87, 88, 94, 95, 96, and 98.

The number 951553 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A105554: Primes whose indices are the sum of the first n+1 Fibonacci numbers.

Number of the day: 67835944

Richard Courant was born on this day 129 years ago.

Properties of the number 67835944:

67835944 = 2³ × 11 × 770863 is the 63837734^th composite number and is not squarefree.
67835944 has 3 distinct prime factors, 16 divisors, 15 antidivisors and 30834480 totatives.
67835944 has a semiprime digit sum 46 in base 10.
67835944 = 16958987² - 16958985² = 8479495² - 8479491² = 1541737² - 1541715² = 770885² - 770841² is the difference of 2 nonnegative squares in 4 ways.
67835944 is the difference of 2 positive pentagonal numbers in 2 ways.
67835944 = 240² + 838² + 8190² is the sum of 3 positive squares.
67835944² is the sum of 3 positive squares.
67835944 is a divisor of 89¹²⁸⁴⁷⁷ - 1.

Number of the day: 91908

Properties of the number 91908:

91908 = 2² × 3³ × 23 × 37 is the 83030^th composite number and is not squarefree.
91908 has 4 distinct prime factors, 48 divisors, 23 antidivisors and 28512 totatives.
91908 = 22978² - 22976² = 7662² - 7656² = 2562² - 2544² = 1022² - 976² = 878² - 824² = 658² - 584² = 402² - 264² = 318² - 96² is the difference of 2 nonnegative squares in 8 ways.
91908 is the difference of 2 positive pentagonal numbers in 1 way.
91908 = 32² + 130² + 272² is the sum of 3 positive squares.
91908² = 29808² + 86940² is the sum of 2 positive squares in 1 way.
91908² is the sum of 3 positive squares.
91908 is a divisor of 919⁴ - 1.
91908 is palindromic in (at least) base -62.
91908 in base 26 = 55oo and consists of only the digits '5' and 'o'.
91908 in base 61 = Ogg and consists of only the digits 'O' and 'g'.

The number 91908 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A121969: Numbers n such that if you subtract n-reversed from n you get a natural number with the same digits as n.
A268346: Number of partitions of (3, n) into a sum of distinct pairs.

Number of the day: 661851787

Properties of the number 661851787:

661851787 is the 34377471^th prime.
661851787 has 31 antidivisors and 661851786 totatives.
661851787 has an emirpimes digit sum 49 in base 10.
Reversing the decimal digits of 661851787 results in a semiprime.
661851787 = 330925894² - 330925893² is the difference of 2 nonnegative squares in 1 way.
661851787 is the sum of 2 positive triangular numbers.
661851787 is the difference of 2 positive pentagonal numbers in 1 way.
661851787 = 579² + 2365² + 25611² is the sum of 3 positive squares.
661851787² is the sum of 3 positive squares.
661851787 is a divisor of 293⁴⁵²⁷⁰³ - 1.
661851787 = '66' + '1851787' is the concatenation of 2 sphenic numbers.
661851787 is an emirp in (at least) the following bases: 17, 18, 35, 39, 51, 53, 58, 61, 70, 79, 84, 85, and 91.

Number of the day: 420723

Camille Jordan was born on this day 179 years ago.

Properties of the number 420723:

420723 = 3² × 46747 is the 385279^th composite number and is not squarefree.
420723 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 280476 totatives.
420723 = 210362² - 210361² = 70122² - 70119² = 23378² - 23369² is the difference of 2 nonnegative squares in 3 ways.
420723 is the sum of 2 positive triangular numbers.
420723 is the difference of 2 positive pentagonal numbers in 1 way.
420723 = 7² + 85² + 643² is the sum of 3 positive squares.
420723² is the sum of 3 positive squares.
420723 is a divisor of 173¹²⁶ - 1.
420723 is palindromic in (at least) the following bases: 78, 85, and -82.

Number of the day: 971951

Sir Isaac Newton was born on this day 374 years ago.

Properties of the number 971951:

971951 is the 76500^th prime.
971951 has 13 antidivisors and 971950 totatives.
Reversing the decimal digits of 971951 results in an emirp.
971951 = 485976² - 485975² is the difference of 2 nonnegative squares in 1 way.
971951 is the difference of 2 positive pentagonal numbers in 1 way.
971951 is not the sum of 3 positive squares.
971951² is the sum of 3 positive squares.
971951 is a divisor of 419¹³⁸⁸⁵ - 1.
971951 = '97' + '1951' is the concatenation of 2 prime numbers.
971951 is an emirp in (at least) the following bases: 3, 4, 5, 7, 8, 10, 13, 27, 30, 53, 56, 64, 67, 71, 90, 91, 92, and 100.

Number of the day: 612931162

Properties of the number 612931162:

612931162 = 2 × 306465581 is semiprime and squarefree.
612931162 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 306465580 totatives.
612931162 has an emirp digit sum 31 in base 10.
612931162 is the difference of 2 positive pentagonal numbers in 2 ways.
612931162 = 2499² + 24631² is the sum of 2 positive squares in 1 way.
612931162 = 385² + 816² + 24741² is the sum of 3 positive squares.
612931162² = 123105738² + 600441160² is the sum of 2 positive squares in 1 way.
612931162² is the sum of 3 positive squares.
612931162 is a divisor of 1051¹⁶⁹³¹⁸ - 1.
612931162 = '6' + '12931162' is the concatenation of 2 semiprime numbers.
612931162 is an emirpimes in (at least) the following bases: 5, 13, 19, 22, 26, 31, 35, 36, 41, 50, 55, 57, 59, 66, 73, 85, 86, and 89.

Number of the day: 783825

Properties of the number 783825:

783825 = 3 × 5² × 7 × 1493 is the 721066^th composite number and is not squarefree.
783825 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 358080 totatives.
783825 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 783825 results in a semiprime.
783825 is the difference of 2 nonnegative squares in 12 ways.
783825 is the sum of 2 positive triangular numbers.
783825 is the difference of 2 positive pentagonal numbers in 5 ways.
783825 = 29² + 110² + 878² is the sum of 3 positive squares.
783825² = 279300² + 732375² = 215985² + 753480² = 418320² + 662865² = 473193² + 624876² = 63063² + 781284² = 470295² + 627060² = 219471² + 752472² is the sum of 2 positive squares in 7 ways.
783825² is the sum of 3 positive squares.
783825 is a divisor of 1061⁶⁰ - 1.
783825 = '7838' + '25' is the concatenation of 2 semiprime numbers.

Number of the day: 2017

Happy New Year!

Properties of the number 2017:

2017 is the 306^th prime.
2017 has 9 antidivisors and 2016 totatives.
2017 has a semiprime digit sum 10 in base 10.
2017 has a triangular digit sum 10 in base 10.
2017 has sum of divisors equal to 2018 which is an emirpimes.
Reversing the decimal digits of 2017 results in a sphenic number.
2017 = 1009² - 1008² is the difference of 2 nonnegative squares in 1 way.
2017 is the sum of 2 positive triangular numbers.
2017 is the difference of 2 positive pentagonal numbers in 1 way.
2017 = 9² + 44² is the sum of 2 positive squares in 1 way.
2017 = 21² + 26² + 30² is the sum of 3 positive squares.
2017² = 792² + 1855² is the sum of 2 positive squares in 1 way.
2017² is the sum of 3 positive squares.
2017 is a divisor of 229⁴ - 1.
2017 is an emirp in (at least) the following bases: 2, 3, 4, 7, 8, 9, 12, 16, 17, 19, 25, 33, 34, 37, 38, 45, 47, 49, 53, 54, 57, 59, 61, 64, 67, 68, 71, 74, 75, 77, 79, 83, 89, 92, 95, and 97.
2017 is palindromic in (at least) the following bases: 31, 32, 36, 42, -8, -48, -56, -63, -72, -84, and -96.
2017 in base 30 = 277 and consists of only the digits '2' and '7'.
2017 in base 31 = 232 and consists of only the digits '2' and '3'.
2017 in base 32 = 1v1 and consists of only the digits '1' and 'v'.
2017 in base 35 = 1mm and consists of only the digits '1' and 'm'.
2017 in base 36 = 1k1 and consists of only the digits '1' and 'k'.
2017 in base 41 = 188 and consists of only the digits '1' and '8'.
2017 in base 42 = 161 and consists of only the digits '1' and '6'.
2017 in base 44 = 11b and consists of only the digits '1' and 'b'.

The number 2017 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005108: Class 4+ primes (for definition see A005105).
A005383: Numbers n such that both n and (n+1)/2 are primes.
A028916: Friedlander-Iwaniec primes: Primes of form a^2 + b^4.
A033215: Primes of form x^2+21*y^2.
A049774: Number of permutations of n elements not containing the consecutive pattern 123.
A107008: Primes of the form x^2+24*y^2.
A142006: Primes congruent to 2 mod 31.
A212959: Number of (w,x,y) such that w,x,y are all in {0,...,n} and |w-x|=|x-y|.
A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.
A242784: Number A(n,k) of permutations of [n] avoiding the consecutive step pattern given by the binary expansion of k, where 1=up and 0=down; square array A(n,k), n>=0, k>=0, read by antidiagonals.