Number of the day: 4991

Properties of the number 4991:

4991 = 7 × 23 × 31 is a sphenic number and squarefree.
4991 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 3960 totatives.
4991 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 4991 results in a semiprime.
4991 = 2496² - 2495² = 360² - 353² = 120² - 97² = 96² - 65² is the difference of 2 nonnegative squares in 4 ways.
4991 is the difference of 2 positive pentagonal numbers in 3 ways.
4991 is not the sum of 3 positive squares.
4991² is the sum of 3 positive squares.
4991 is a divisor of 1427² - 1.
4991 = '49' + '91' is the concatenation of 2 semiprime numbers.
4991 is palindromic in (at least) the following bases: 19, -28, and -43.
4991 in base 19 = dfd and consists of only the digits 'd' and 'f'.

The number 4991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001845: Centered octahedral numbers (crystal ball sequence for cubic lattice).
A004006: C(n,1) + C(n,2) + C(n,3), or n*(n^2+5)/6.
A005008: n! - n^2.
A006972: Lucas-Carmichael numbers: squarefree composite numbers n such that p | n => p+1 | n+1.
A152942: Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 4.
A195575: Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2/5.
A199118: Number of partitions of n into terms of (1,3)-Ulam sequence, cf. A002859.
A216925: Lucas-Carmichael numbers with 3 prime factors.
A257752: Quasi-Carmichael numbers to exactly two bases.
A263799: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing

Number of the day: 1337

Properties of the number 1337:

1337 = 7 × 191 is semiprime and squarefree.
1337 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 1140 totatives.
1337 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 1337 results in a prime.
1337 = 669² - 668² = 99² - 92² is the difference of 2 nonnegative squares in 2 ways.
1337 is the difference of 2 positive pentagonal numbers in 2 ways.
1337 = 4² + 5² + 36² is the sum of 3 positive squares.
1337² is the sum of 3 positive squares.
1337 is a divisor of 421⁵ - 1.
1337 = '13' + '37' is the concatenation of 2 emirps.
1337 is an emirpimes in (at least) the following bases: 2, 5, 7, 9, 17, 23, 27, 28, 29, 30, 37, 38, 40, 41, 42, 43, 44, 45, 49, 55, 59, 60, 61, 62, 66, 67, 71, 75, 76, 77, 81, 82, 83, 84, 91, 93, 95, 96, 98, 99, and 100.
1337 is palindromic in (at least) the following bases: -14, -18, and -23.
1337 in base 3 = 1211112 and consists of only the digits '1' and '2'.
1337 in base 13 = 7bb and consists of only the digits '7' and 'b'.
1337 in base 36 = 115 and consists of only the digits '1' and '5'.

The number 1337 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033681: a(1) = 3; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A075928: List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.
A084600: Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+x+2x^2)^n for n>=0.
A121027: Multiples of 7 containing a 7 in their decimal representation.
A162527: Numbers n such that their largest divisor <= sqrt(n) equals 7.
A191450: Dispersion of (3n-1), read by antidiagonals.
A239405: T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4
A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
A254100: Postludic numbers: Second column of Ludic array A255127.
A256082: Non-palindromic balanced numbers in base 2.

Number of the day: 4018282980

Properties of the number 4018282980:

4018282980 = 2² × 3 × 5 × 53 × 101 × 12511 is the 3827495000^th composite number and is not squarefree.
4018282980 has 6 distinct prime factors, 96 divisors, 37 antidivisors and 1040832000 totatives.
4018282980 has a sphenic digit sum 42 in base 10.
4018282980 has an oblong digit sum 42 in base 10.
4018282980 is the difference of 2 nonnegative squares in 16 ways.
4018282980 is the difference of 2 positive pentagonal numbers in 6 ways.
4018282980 = 370² + 2684² + 63332² is the sum of 3 positive squares.
4018282980² = 2756423520² + 2923820700² = 450846396² + 3992910672² = 685202448² + 3959431236² = 1726668132² + 3628390176² = 795699600² + 3938713020² = 2673550656² + 2999787492² = 1405235520² + 3764559900² = 1134547524² + 3854789232² = 2168506608² + 3382924356² = 2122866480² + 3411749700² = 348756636² + 4003119648² = 1455679872² + 3745343004² = 2410969788² + 3214626384² is the sum of 2 positive squares in 13 ways.
4018282980² is the sum of 3 positive squares.
4018282980 is a divisor of 1229¹¹⁷⁰ - 1.

Number of the day: 81326848

Giuseppe Peano was born on this day 158 years ago.

Properties of the number 81326848:

81326848 = 2⁸ × 107 × 2969 is the 76584398^th composite number and is not squarefree.
81326848 has 3 distinct prime factors, 36 divisors, 23 antidivisors and 40269824 totatives.
81326848 is the difference of 2 nonnegative squares in 14 ways.
81326848 is the sum of 2 positive triangular numbers.
81326848 is the difference of 2 positive pentagonal numbers in 1 way.
81326848 = 304² + 816² + 8976² is the sum of 3 positive squares.
81326848² = 6327552² + 81080320² is the sum of 2 positive squares in 1 way.
81326848² is the sum of 3 positive squares.
81326848 is a divisor of 1663²¹² - 1.

Number of the day: 6545

Properties of the number 6545:

6545 = 5 × 7 × 11 × 17 is the 5700^th composite number and is squarefree.
6545 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 3840 totatives.
6545 has an oblong digit sum 20 in base 10.
6545 has an oblong digit product 600 in base 10.
6545 = 11² + … + 27² is the sum of at least 2 consecutive positive squares in 1 way.
6545 = (1 × 2)/2 + … + (33 × 34)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6545 = 3273² - 3272² = 657² - 652² = 471² - 464² = 303² - 292² = 201² - 184² = 111² - 76² = 87² - 32² = 81² - 4² is the difference of 2 nonnegative squares in 8 ways.
6545 is the sum of 2 positive triangular numbers.
6545 is the difference of 2 positive pentagonal numbers in 6 ways.
6545 = 10² + 19² + 78² is the sum of 3 positive squares.
6545² = 3080² + 5775² = 1001² + 6468² = 2772² + 5929² = 3927² + 5236² is the sum of 2 positive squares in 4 ways.
6545² is the sum of 3 positive squares.
6545 is a divisor of 1429² - 1.
6545 = '6' + '545' is the concatenation of 2 semiprime numbers.
6545 is palindromic in (at least) the following bases: 16, 21, 84, and -23.
6545 in base 16 = 1991 and consists of only the digits '1' and '9'.
6545 in base 21 = ehe and consists of only the digits 'e' and 'h'.
6545 in base 22 = dbb and consists of only the digits 'b' and 'd'.

The number 6545 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000292: Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.
A000447: a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.
A013594: Smallest order of cyclotomic polynomial containing n or -n as a coefficient.
A092269: Spt function: total number of smallest parts in all partitions of n.
A134605: Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.
A135602: Right-angled numbers with an internal digit as the vertex.
A138135: Number of parts > 1 in the last section of the set of partitions of n.
A152977: Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the number of partitions of 2^n into powers of 2 less than or equal to 2^k.
A248068: T(n,k)=Number of length n+5 0..k arrays with some disjoint triples in each consecutive six terms having the same sum
A255872: Smallest Rhonda number to base b = n-th composite number, cf. A002808.

Number of the day: 34384

Properties of the number 34384:

34384 = 2⁴ × 7 × 307 is the 30708^th composite number and is not squarefree.
34384 has 3 distinct prime factors, 20 divisors, 13 antidivisors and 14688 totatives.
34384 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 34384 results in a semiprime.
34384 = 8597² - 8595² = 4300² - 4296² = 2153² - 2145² = 1235² - 1221² = 628² - 600² = 335² - 279² is the difference of 2 nonnegative squares in 6 ways.
34384 is the sum of 2 positive triangular numbers.
34384 is the difference of 2 positive pentagonal numbers in 2 ways.
34384 = 72² + 92² + 144² is the sum of 3 positive squares.
34384² is the sum of 3 positive squares.
34384 is a divisor of 17⁶ - 1.
34384 is palindromic in (at least) the following bases: 33, 52, and 90.
34384 in base 33 = viv and consists of only the digits 'i' and 'v'.
34384 in base 52 = CbC and consists of only the digits 'C' and 'b'.
34384 in base 53 = CCe and consists of only the digits 'C' and 'e'.

The number 34384 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057546: Number of Catalan objects of size n fixed by Catalan Automorphism A057511/A057512 (deep rotation of general parenthesizations/plane trees).
A059376: Jordan function J_3(n).
A063453: Multiplicative with a(p^e) = 1 - p^3.
A082261: Row sums in A082259.
A192349: Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
A211689: Number of -4..4 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two or three distinct values for every i<=n and j<=n

Number of the day: 3548

Properties of the number 3548:

3548 = 2² × 887 is the 3050^th composite number and is not squarefree.
3548 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 1772 totatives.
3548 has an oblong digit sum 20 in base 10.
3548 has sum of divisors equal to 6216 which is a triangular number.
Reversing the decimal digits of 3548 results in a semiprime.
3548 = 888² - 886² is the difference of 2 nonnegative squares in 1 way.
3548 is the difference of 2 positive pentagonal numbers in 1 way.
3548 is not the sum of 3 positive squares.
3548² is the sum of 3 positive squares.
3548 is a divisor of 13⁴⁴³ - 1.
3548 is palindromic in (at least) the following bases: 17, 20, and 23.
3548 in base 16 = ddc and consists of only the digits 'c' and 'd'.
3548 in base 17 = c4c and consists of only the digits '4' and 'c'.
3548 in base 20 = 8h8 and consists of only the digits '8' and 'h'.
3548 in base 22 = 776 and consists of only the digits '6' and '7'.
3548 in base 23 = 6g6 and consists of only the digits '6' and 'g'.
3548 in base 59 = 118 and consists of only the digits '1' and '8'.

The number 3548 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000954: Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.
A008509: Numbers n such that n-th triangular number is palindromic.
A053618: a(n) = ceiling(C(n,4)/n).
A066321: Binary representation of base i-1 expansion of n: replace i-1 by 2 in base i-1 expansion of n.
A127764: Integer part of Gauss' Arithmetic-Geometric Mean M(2,n^3).
A234500: Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
A245173: Triangle read by rows: coefficients of the polynomials A_{3,4}(n,k).
A252993: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly 2 distinct values, in every diagonal 1 or 2 distinct values, in every antidiagonal 2 or 3 distinct values, and new values 0 upwards introduced in row major order
A261761: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column prime, read as a binary number with top and left being the most significant bits.
A270980: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 237", based on the 5-celled von Neumann neighborhood.

Number of the day: 6165

Properties of the number 6165:

6165 = 3² × 5 × 137 is the 5361^th composite number and is not squarefree.
6165 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 3264 totatives.
6165 = (30 × 31)/2 + … + (39 × 40)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6165 = 3083² - 3082² = 1029² - 1026² = 619² - 614² = 347² - 338² = 213² - 198² = 91² - 46² is the difference of 2 nonnegative squares in 6 ways.
6165 is the difference of 2 positive pentagonal numbers in 1 way.
6165 = 54² + 57² = 9² + 78² is the sum of 2 positive squares in 2 ways.
6165 = 10² + 17² + 76² is the sum of 3 positive squares.
6165² = 3960² + 4725² = 333² + 6156² = 1404² + 6003² = 3699² + 4932² is the sum of 2 positive squares in 4 ways.
6165² is the sum of 3 positive squares.
6165 is a divisor of 37⁴ - 1.
6165 is palindromic in (at least) the following bases: 35, 67, -27, and -92.
6165 in base 26 = 933 and consists of only the digits '3' and '9'.
6165 in base 34 = 5bb and consists of only the digits '5' and 'b'.
6165 in base 35 = 515 and consists of only the digits '1' and '5'.
6165 in base 55 = 225 and consists of only the digits '2' and '5'.

The number 6165 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045944: Rhombic matchstick numbers: n*(3*n+2).
A061541: Number of connected labeled graphs with n nodes and n+2 edges.
A062734: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, 0 <= k <= n(n-1)/2).
A073399: Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073400.
A123527: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, n-1 <= k <= n(n-1)/2).
A164000: Main diagonal of array in A163280.
A166512: 2-comma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for two different splittings n=concat(S[0],S[1]).
A214359: Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
A228024: Antiharmonic mean of the divisors of A228023(n) (the n-th primitive antiharmonic number).
A262521: Numbers where A262520 takes a negative value; numbers n for which A155043(2n) > A155043(2n + 1).

Number of the day: 828606

Properties of the number 828606:

828606 = 2 × 3 × 138101 is a sphenic number and squarefree.
828606 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 276200 totatives.
828606 has a sphenic digit sum 30 in base 10.
828606 has an oblong digit sum 30 in base 10.
828606 is the sum of 2 positive triangular numbers.
828606 is the difference of 2 positive pentagonal numbers in 2 ways.
828606 = 5² + 166² + 895² is the sum of 3 positive squares.
828606² = 215694² + 800040² is the sum of 2 positive squares in 1 way.
828606² is the sum of 3 positive squares.
828606 is a divisor of 751¹³⁸¹ - 1.

Number of the day: 9794

Augustin-Louis Cauchy was born on this day 227 years ago.

Properties of the number 9794:

9794 = 2 × 59 × 83 is a sphenic number and squarefree.
9794 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 4756 totatives.
9794 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 9794 results in a semiprime.
9794 is the difference of 2 positive pentagonal numbers in 1 way.
9794 = 12² + 25² + 95² is the sum of 3 positive squares.
9794² is the sum of 3 positive squares.
9794 is a divisor of 167²⁹ - 1.
9794 = '9' + '794' is the concatenation of 2 semiprime numbers.
9794 is palindromic in (at least) the following bases: 64, 68, -23, -55, -72, and -96.

The number 9794 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A010007: a(0) = 1, a(n) = 17*n^2 + 2 for n>0.
A031596: Numbers n such that continued fraction for sqrt(n) has even period and central term 98.
A060168: Number of orbits of length n under the map whose periodic points are counted by A001643.
A137411: Weak Goodstein sequence starting at 11.
A164217: Number of binary strings of length n with equal numbers of 00010 and 01011 substrings
A244474: 4th-largest term in n-th row of Stern's diatomic triangle A002487.
A252676: Number of (n+2)X(5+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 5 6 or 7
A252679: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 5 6 or 7
A252682: Number of (3+2)X(n+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 5 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 5 6 or 7
A256034: Number of irreducible idempotents in partition monoid P_n.

Number of the day: 33142

Properties of the number 33142:

33142 = 2 × 73 × 227 is a sphenic number and squarefree.
33142 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 16272 totatives.
33142 has an emirp digit sum 13 in base 10.
33142 has a Fibonacci digit sum 13 in base 10.
33142 has an oblong digit product 72 in base 10.
Reversing the decimal digits of 33142 results in a prime.
33142 is the difference of 2 positive pentagonal numbers in 3 ways.
33142 = 18² + 97² + 153² is the sum of 3 positive squares.
33142² = 21792² + 24970² is the sum of 2 positive squares in 1 way.
33142² is the sum of 3 positive squares.
33142 is a divisor of 907⁷² - 1.
33142 = '33' + '142' is the concatenation of 2 semiprime numbers.
33142 is palindromic in (at least) the following bases: -3, and -76.
33142 in base 45 = GGM and consists of only the digits 'G' and 'M'.

The number 33142 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A164420: Number of binary strings of length n with no substrings equal to 0000 0010 or 0111
A247865: Numbers n such that n!3 + 3^2 is prime.

Number of the day: 490415

Properties of the number 490415:

490415 = 5 × 43 × 2281 is a sphenic number and squarefree.
490415 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 383040 totatives.
490415 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 490415 results in a sphenic number.
490415 = 245208² - 245207² = 49044² - 49039² = 5724² - 5681² = 1248² - 1033² is the difference of 2 nonnegative squares in 4 ways.
490415 is the difference of 2 positive pentagonal numbers in 4 ways.
490415 is not the sum of 3 positive squares.
490415² = 309600² + 380335² = 19479² + 490028² = 118508² + 475881² = 294249² + 392332² is the sum of 2 positive squares in 4 ways.
490415² is the sum of 3 positive squares.
490415 is a divisor of 251⁵⁷ - 1.

Number of the day: 40726715

Properties of the number 40726715:

40726715 = 5 × 31 × 103 × 2551 is the 38251554^th composite number and is squarefree.
40726715 has 4 distinct prime factors, 16 divisors, 39 antidivisors and 31212000 totatives.
40726715 = 20363358² - 20363357² = 4072674² - 4072669² = 656898² - 656867² = 197754² - 197651² = 131454² - 131299² = 39798² - 39283² = 9258² - 6707² = 7974² - 4781² is the difference of 2 nonnegative squares in 8 ways.
40726715 is the difference of 2 positive pentagonal numbers in 7 ways.
40726715 = 85² + 231² + 6377² is the sum of 3 positive squares.
40726715² = 24436029² + 32581372² is the sum of 2 positive squares in 1 way.
40726715² is the sum of 3 positive squares.
40726715 is a divisor of 1499¹⁵⁰ - 1.
40726715 = '40726' + '715' is the concatenation of 2 sphenic numbers.

Number of the day: 346759

Pierre de Fermat was born on this day 415 years ago.

Properties of the number 346759:

346759 = 7 × 49537 is semiprime and squarefree.
346759 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 297216 totatives.
346759 has a semiprime digit sum 34 in base 10.
346759 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 346759 results in a prime.
346759 = 173380² - 173379² = 24772² - 24765² is the difference of 2 nonnegative squares in 2 ways.
346759 is the sum of 2 positive triangular numbers.
346759 is the difference of 2 positive pentagonal numbers in 2 ways.
346759 is not the sum of 3 positive squares.
346759² = 235865² + 254184² is the sum of 2 positive squares in 1 way.
346759² is the sum of 3 positive squares.
346759 is a divisor of 991³⁸⁴ - 1.
346759 = '3467' + '59' is the concatenation of 2 prime numbers.
346759 is an emirpimes in (at least) the following bases: 5, 9, 16, 17, 19, 22, 23, 29, 31, 32, 35, 46, 47, 55, 56, 61, 67, 68, 74, 77, 79, 80, 81, 82, 84, 85, 87, 91, and 97.
346759 is palindromic in (at least) base 6.
346759 in base 3 = 122121122221 and consists of only the digits '1' and '2'.

Number of the day: 2709947

Arthur Cayley was born on this day 195 years ago.

Properties of the number 2709947:

2709947 = 439 × 6173 is semiprime and squarefree.
2709947 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2703336 totatives.
2709947 has a semiprime digit sum 38 in base 10.
2709947 = 1354974² - 1354973² = 3306² - 2867² is the difference of 2 nonnegative squares in 2 ways.
2709947 is the sum of 2 positive triangular numbers.
2709947 is the difference of 2 positive pentagonal numbers in 2 ways.
2709947 = 51² + 145² + 1639² is the sum of 3 positive squares.
2709947² = 243645² + 2698972² is the sum of 2 positive squares in 1 way.
2709947² is the sum of 3 positive squares.
2709947 is a divisor of 877³⁰⁸⁶ - 1.
2709947 is an emirpimes in (at least) the following bases: 3, 5, 7, 8, 9, 11, 17, 25, 27, 29, 31, 33, 36, 40, 47, 50, 53, 55, 56, 57, 59, 61, 63, 66, 70, 71, 77, 81, 88, 92, 94, 95, and 97.

Number of the day: 326158

Properties of the number 326158:

326158 = 2 × 7 × 23297 is a sphenic number and squarefree.
326158 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 139776 totatives.
326158 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 326158 results in a prime.
326158 is the difference of 2 positive pentagonal numbers in 4 ways.
326158 = 51² + 94² + 561² is the sum of 3 positive squares.
326158² = 104370² + 309008² is the sum of 2 positive squares in 1 way.
326158² is the sum of 3 positive squares.
326158 is a divisor of 317⁹⁶ - 1.
326158 = '326' + '158' is the concatenation of 2 emirpimes.
326158 is palindromic in (at least) base -75.

Number of the day: 583

Properties of the number 583:

583 = 11 × 53 is semiprime and squarefree.
583 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 520 totatives.
583 has a triangular digit product 120 in base 10.
Reversing the decimal digits of 583 results in a sphenic number.
583 = 292² - 291² = 32² - 21² is the difference of 2 nonnegative squares in 2 ways.
583 is the sum of 2 positive triangular numbers.
583 is the difference of 2 positive pentagonal numbers in 1 way.
583 is not the sum of 3 positive squares.
583² = 308² + 495² is the sum of 2 positive squares in 1 way.
583² is the sum of 3 positive squares.
583 is a divisor of 23⁴ - 1.
583 = '5' + '83' is the concatenation of 2 prime numbers.
583 is an emirpimes in (at least) the following bases: 2, 3, 4, 6, 13, 15, 16, 21, 23, 24, 27, 31, 34, 39, 40, 44, 46, 47, 49, 50, 51, 59, 60, 65, 69, 70, 71, 73, 76, 78, 82, 88, 89, 92, 95, 98, and 99.
583 is palindromic in (at least) the following bases: 9, 52, -4, and -97.
583 in base 9 = 717 and consists of only the digits '1' and '7'.

The number 583 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008484: Number of partitions of n into parts >= 4.
A008593: Multiples of 11.
A036952: Numbers whose binary expansion is a decimal prime.
A051349: Sum of first n nonprimes.
A069605: a(1) = 3; a(n) = smallest number such that the concatenation a(1)a(2)...a(n) is a prime.
A078972: Brilliant numbers: semiprimes (products of two primes, A001358) whose prime factors have the same number of decimal digits.
A160120: Y-toothpick sequence (see Comments lines for definition).
A181470: Numbers n such that 97 is the largest prime factor of n^2-1.
A195160: Generalized 11-gonal numbers.
A235227: Numbers whose sum of digits is 16.

Number of the day: 2113

Properties of the number 2113:

2111 and 2113 form a twin prime pair.
2113 has 10 antidivisors and 2112 totatives.
2113 has a prime digit sum 7 in base 10.
2113 has a semiprime digit product 6 in base 10.
2113 has a triangular digit product 6 in base 10.
2113 has an oblong digit product 6 in base 10.
2113 has sum of divisors equal to 2114 which is a sphenic number.
2113 = 32² + 33² is the sum of at least 2 consecutive positive squares in 1 way.
2113 = 1057² - 1056² is the difference of 2 nonnegative squares in 1 way.
2113 is the difference of 2 positive pentagonal numbers in 1 way.
2113 = 32² + 33² is the sum of 2 positive squares in 1 way.
2113 = 5² + 18² + 42² is the sum of 3 positive squares.
2113² = 65² + 2112² is the sum of 2 positive squares in 1 way.
2113² is the sum of 3 positive squares.
2113 is a divisor of 439⁶ - 1.
2113 = '2' + '113' is the concatenation of 2 prime numbers.
2113 = '21' + '13' is the concatenation of 2 Fibonacci numbers.
2113 is an emirp in (at least) the following bases: 2, 11, 19, 21, 25, 26, 29, 31, 34, 37, 40, 42, 43, 45, 49, 51, 53, 55, 56, 64, 71, 76, 81, 84, 85, 89, 95, 97, and 100.
2113 is palindromic in (at least) the following bases: 33, 44, -18, -48, -64, -66, -88, and -96.
2113 in base 14 = aad and consists of only the digits 'a' and 'd'.
2113 in base 17 = 755 and consists of only the digits '5' and '7'.
2113 in base 20 = 55d and consists of only the digits '5' and 'd'.
2113 in base 26 = 337 and consists of only the digits '3' and '7'.
2113 in base 32 = 221 and consists of only the digits '1' and '2'.
2113 in base 33 = 1v1 and consists of only the digits '1' and 'v'.
2113 in base 43 = 166 and consists of only the digits '1' and '6'.
2113 in base 44 = 141 and consists of only the digits '1' and '4'.
2113 in base 45 = 11h and consists of only the digits '1' and 'h'.

The number 2113 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001844: Centered square numbers: 2n(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.
A005108: Class 4+ primes (for definition see A005105).
A027862: Primes of the form n^2 + (n+1)^2.
A053001: Largest prime < n^2.
A061068: Primes which are the sum of a prime and its subscript.
A069489: Primes > 1000 in which every substring of length 3 is also prime.
A090707: Primes whose decimal representation is a valid number in base 4 and interpreted as such is again a prime.
A107008: Primes of the form x^2+24*y^2.
A211684: Numbers > 1000 such that all the substrings of length = 3 are primes (substrings with leading '0' are considered to be nonprime).
A211685: Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).

Number of the day: 662909031402

Properties of the number 662909031402:

662909031402 = 2 × 3 × 17 × 6499108151 is composite and squarefree.
662909031402 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 207971460800 totatives.
662909031402 has a sphenic digit sum 42 in base 10.
662909031402 has an oblong digit sum 42 in base 10.
662909031402 is the sum of 2 positive triangular numbers.
662909031402 is the difference of 2 positive pentagonal numbers in 2 ways.
662909031402 = 757² + 3808² + 814183² is the sum of 3 positive squares.
662909031402² = 311957191248² + 584919733590² is the sum of 2 positive squares in 1 way.
662909031402² is the sum of 3 positive squares.
662909031402 is a divisor of 1231^39004400 - 1.
662909031402 = '66' + '2909031402' is the concatenation of 2 sphenic numbers.

Number of the day: 74066

Properties of the number 74066:

74066 = 2 × 29 × 1277 is a sphenic number and squarefree.
74066 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 35728 totatives.
74066 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 74066 results in a prime.
74066 is the difference of 2 positive pentagonal numbers in 2 ways.
74066 = 179² + 205² = 25² + 271² is the sum of 2 positive squares in 2 ways.
74066 = 29² + 44² + 267² is the sum of 3 positive squares.
74066² = 51080² + 53634² = 13550² + 72816² = 9984² + 73390² = 43384² + 60030² is the sum of 2 positive squares in 4 ways.
74066² is the sum of 3 positive squares.
74066 is a divisor of 347²² - 1.
74066 is palindromic in (at least) the following bases: 59, 64, and -57.
74066 in base 42 = ffK and consists of only the digits 'K' and 'f'.
74066 in base 56 = NYY and consists of only the digits 'N' and 'Y'.
74066 in base 59 = LGL and consists of only the digits 'G' and 'L'.

The number 74066 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A031609: Numbers n such that continued fraction for sqrt(n) has odd period and central terms 21.

Number of the day: 95503

Properties of the number 95503:

95503 = 43 × 2221 is semiprime and squarefree.
95503 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 93240 totatives.
95503 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 95503 results in a prime.
95503 = 47752² - 47751² = 1132² - 1089² is the difference of 2 nonnegative squares in 2 ways.
95503 is the difference of 2 positive pentagonal numbers in 2 ways.
95503 is not the sum of 3 positive squares.
95503² = 54180² + 78647² is the sum of 2 positive squares in 1 way.
95503² is the sum of 3 positive squares.
95503 is a divisor of 317⁸⁴ - 1.
95503 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 15, 16, 21, 22, 25, 26, 29, 30, 31, 33, 35, 37, 39, 41, 44, 46, 47, 50, 55, 56, 57, 61, 66, 73, 75, 81, 83, 84, 85, 89, 90, and 96.
95503 in base 51 = aaV and consists of only the digits 'V' and 'a'.
95503 in base 55 = VVN and consists of only the digits 'N' and 'V'.

The number 95503 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005651: Sum of multinomial coefficients (n_1+n_2+...)!/(n_1!*n_2!*...).
A152536: Sum_{k=0..binomial(n,2)}(-1)^k*A152534(n,k).
A183610: Rectangular table where T(n,k) is the sum of the n-th powers of the k-th row of multinomial coefficients in triangle A036038 for n>=0, k>=0, as read by antidiagonals.
A226878: Number of n-length words w over a 8-ary alphabet {a1,a2,...,a8} such that #(w,a1) >= #(w,a2) >= ... >= #(w,a8) >= 0, where #(w,x) counts the number of letters x in word w.
A226879: Number of n-length words w over a 9-ary alphabet {a1,a2,...,a9} such that #(w,a1) >= #(w,a2) >= ... >= #(w,a9) >= 0, where #(w,x) counts the number of letters x in word w.
A226880: Number of n-length words w over a 10-ary alphabet {a1,a2,...,a10} such that #(w,a1) >= #(w,a2) >= ... >= #(w,a10) >= 0, where #(w,x) counts the number of letters x in word w.
A261719: Number T(n,k) of partitions of n where each part i is marked with a word of length i over a k-ary alphabet whose letters appear in alphabetical order and all k letters occur at least once in the partition; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

Number of the day: 33181367739250

Properties of the number 33181367739250:

33181367739250 = 2 × 5³ × 19 × 53 × 131802851 is composite and not squarefree.
33181367739250 has 5 distinct prime factors, 64 divisors, 59 antidivisors and 12336746760000 totatives.
33181367739250 has an emirpimes digit sum 58 in base 10.
33181367739250 is the difference of 2 positive pentagonal numbers in 16 ways.
33181367739250 = 225² + 736² + 5760327² is the sum of 3 positive squares.
33181367739250² = 19908820643550² + 26545094191400² = 12020420011200² + 30927538987150² = 2879892294350² + 33056155030800² = 17529779183000² + 28172859401250² = 22137606853960² + 24716988648030² = 9290782966990² + 31854113029680² = 8940187383330² + 31954283196440² = 20199314127154² + 26324719824528² = 11679841444216² + 31057760203938² = 6491026806048² + 32540278671986² is the sum of 2 positive squares in 10 ways.
33181367739250² is the sum of 3 positive squares.
33181367739250 is a divisor of 929^78278850 - 1.

Number of the day: 32582202105

Properties of the number 32582202105:

32582202105 = 3 × 5 × 71 × 1409 × 21713 is composite and squarefree.
32582202105 has 5 distinct prime factors, 32 divisors, 37 antidivisors and 17119477760 totatives.
32582202105 has a sphenic digit sum 30 in base 10.
32582202105 has an oblong digit sum 30 in base 10.
32582202105 is the difference of 2 nonnegative squares in 16 ways.
32582202105 is the difference of 2 positive pentagonal numbers in 7 ways.
32582202105 = 487² + 1970² + 180494² is the sum of 3 positive squares.
32582202105² = 13318472520² + 29735806425² = 7186705839² + 31779728652² = 15797561628² + 28496261871² = 16483033116² + 28105328913² = 3676770855² + 32374083000² = 22365866484² + 23693203887² = 19647537480² + 25991809575² = 122944239² + 32581970148² = 9004925172² + 31313115729² = 16588967175² + 28042932480² = 3554585748² + 32387726289² = 12480965679² + 30096933228² = 19549321263² + 26065761684² is the sum of 2 positive squares in 13 ways.
32582202105² is the sum of 3 positive squares.
32582202105 is a divisor of 709¹⁰³⁸⁴ - 1.
32582202105 = '32582' + '202105' is the concatenation of 2 sphenic numbers.

Number of the day: 62045

Properties of the number 62045:

62045 = 5 × 12409 is semiprime and squarefree.
62045 has 2 distinct prime factors, 4 divisors, 23 antidivisors and 49632 totatives.
62045 has an emirp digit sum 17 in base 10.
62045 = 31023² - 31022² = 6207² - 6202² is the difference of 2 nonnegative squares in 2 ways.
62045 is the difference of 2 positive pentagonal numbers in 2 ways.
62045 = 98² + 229² = 59² + 242² is the sum of 2 positive squares in 2 ways.
62045 = 10² + 21² + 248² is the sum of 3 positive squares.
62045² = 28556² + 55083² = 10205² + 61200² = 42837² + 44884² = 37227² + 49636² is the sum of 2 positive squares in 4 ways.
62045² is the sum of 3 positive squares.
62045 is a divisor of 773⁸ - 1.
62045 = '6' + '2045' is the concatenation of 2 semiprime numbers.
62045 is an emirpimes in (at least) the following bases: 2, 5, 8, 11, 17, 22, 29, 30, 32, 33, 40, 42, 49, 59, 60, 65, 67, 73, 75, 82, and 93.
62045 is palindromic in (at least) base -69.

The number 62045 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A027154: a(n) = Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A027144.

Number of the day: 8939

Johann Bernoulli was born on this day 349 years ago.

Properties of the number 8939:

8939 = 7 × 1277 is semiprime and squarefree.
8939 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 7656 totatives.
8939 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 8939 results in a sphenic number.
8939 = (47 × 48)/2 + … + (53 × 54)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
8939 = 4470² - 4469² = 642² - 635² is the difference of 2 nonnegative squares in 2 ways.
8939 is the sum of 2 positive triangular numbers.
8939 is the difference of 2 positive pentagonal numbers in 2 ways.
8939 = 17² + 27² + 89² is the sum of 3 positive squares.
8939² = 5236² + 7245² is the sum of 2 positive squares in 1 way.
8939² is the sum of 3 positive squares.
8939 is a divisor of 113⁴ - 1.
8939 = '893' + '9' is the concatenation of 2 semiprime numbers.
8939 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 6, 7, 9, 11, 13, 14, 16, 17, 19, 20, 23, 24, 26, 34, 37, 41, 42, 43, 49, 52, 53, 55, 56, 57, 61, 65, 69, 72, 74, 76, 79, 84, 86, 88, 91, 94, 95, 96, and 98.
8939 is palindromic in (at least) the following bases: 25, 82, and -9.
8939 in base 25 = e7e and consists of only the digits '7' and 'e'.
8939 in base 28 = bb7 and consists of only the digits '7' and 'b'.
8939 in base 31 = 99b and consists of only the digits '9' and 'b'.
8939 in base 54 = 33T and consists of only the digits '3' and 'T'.

The number 8939 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A017822: Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
A041469: Denominators of continued fraction convergents to sqrt(250).
A042937: Denominators of continued fraction convergents to sqrt(1000).
A058366: Number of ways to cover (without overlapping) a ring lattice (necklace) of n sites with molecules that are 7 sites wide.
A069833: Prefixing, suffixing or inserting a 9 in the number anywhere gives a prime.
A089141: Square array, read by antidiagonal: T(n,k) = n*T(n,k-1)+(-1)^k*T(n,floor(k/2)).
A173893: (Average of twin balanced prime pairs)/10.
A184699: Number of strings of numbers x(i=1..n) in 0..5 with sum i*x(i) equal to n*5
A184709: Number of strings of numbers x(i=1..9) in 0..n with sum i*x(i) equal to n*9
A271695: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 398", based on the 5-celled von Neumann neighborhood.

Number of the day: 38613294

Niels Henrik Abel was born on this day 214 years ago.

Properties of the number 38613294:

38613294 = 2 × 3³ × 383 × 1867 is the 36259109^th composite number and is not squarefree.
38613294 has 4 distinct prime factors, 32 divisors, 23 antidivisors and 12830616 totatives.
38613294 has a triangular digit sum 36 in base 10.
38613294 is the sum of 2 positive triangular numbers.
38613294 is the difference of 2 positive pentagonal numbers in 2 ways.
38613294 = 173² + 178² + 6209² is the sum of 3 positive squares.
38613294² is the sum of 3 positive squares.
38613294 is a divisor of 1531¹⁸⁶⁶ - 1.

Number of the day: 89831157176295

William Rowan Hamilton was born on this day 211 years ago.

John Venn was born on this day 182 years ago.

Properties of the number 89831157176295:

89831157176295 = 3² × 5 × 107713 × 18533027 is composite and not squarefree.
89831157176295 has 4 distinct prime factors, 24 divisors, 55 antidivisors and 47909503116288 totatives.
89831157176295 has an oblong digit sum 72 in base 10.
89831157176295 is the difference of 2 nonnegative squares in 12 ways.
89831157176295 is the sum of 2 positive triangular numbers.
89831157176295 is the difference of 2 positive pentagonal numbers in 3 ways.
89831157176295 is not the sum of 3 positive squares.
89831157176295² = 40896515619441² + 79981946774388² = 15271955569080² + 88523466791175² = 61655600091492² + 65331644529969² = 53898694305777² + 71864925741036² is the sum of 2 positive squares in 4 ways.
89831157176295² is the sum of 3 positive squares.
89831157176295 is a divisor of 1097^148264208 - 1.
89831157176295 = '8983115717' + '6295' is the concatenation of 2 semiprime numbers.
89831157176295 = '89831' + '157176295' is the concatenation of 2 sphenic numbers.

Number of the day: 87483

Properties of the number 87483:

87483 = 3 × 11² × 241 is the 78991^th composite number and is not squarefree.
87483 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 52800 totatives.
87483 has a sphenic digit sum 30 in base 10.
87483 has an oblong digit sum 30 in base 10.
87483 = 43742² - 43741² = 14582² - 14579² = 3982² - 3971² = 1342² - 1309² = 422² - 301² = 302² - 61² is the difference of 2 nonnegative squares in 6 ways.
87483 is the sum of 2 positive triangular numbers.
87483 is the difference of 2 positive pentagonal numbers in 2 ways.
87483 = 13² + 17² + 295² is the sum of 3 positive squares.
87483² = 43560² + 75867² is the sum of 2 positive squares in 1 way.
87483² is the sum of 3 positive squares.
87483 is a divisor of 727¹² - 1.
87483 is palindromic in (at least) the following bases: 74, and 88.
87483 in base 3 = 11110000010 and consists of only the digits '0' and '1'.

Number of the day: 450706

Properties of the number 450706:

450706 = 2 × 225353 is semiprime and squarefree.
450706 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 225352 totatives.
450706 has a semiprime digit sum 22 in base 10.
450706 is the sum of 2 positive triangular numbers.
450706 is the difference of 2 positive pentagonal numbers in 2 ways.
450706 = 291² + 605² is the sum of 2 positive squares in 1 way.
450706 = 120² + 241² + 615² is the sum of 3 positive squares.
450706² = 281344² + 352110² is the sum of 2 positive squares in 1 way.
450706² is the sum of 3 positive squares.
450706 is a divisor of 31¹⁶⁵⁷ - 1.
450706 is an emirpimes in (at least) the following bases: 4, 5, 7, 8, 14, 20, 21, 22, 29, 32, 37, 40, 43, 50, 52, 60, 61, 64, 66, 72, 74, 75, 76, 77, 83, 85, 87, 91, 92, 93, 95, 97, and 100.
450706 is palindromic in (at least) base 88.

Number of the day: 2198

Properties of the number 2198:

2198 = 2 × 7 × 157 is a sphenic number and squarefree.
2198 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 936 totatives.
2198 has an oblong digit sum 20 in base 10.
2198 has a Fibonacci digit product 144 in base 10.
2198 = 13³ + 1³ is the sum of 2 positive cubes in 1 way.
2198 is the sum of 2 positive triangular numbers.
2198 = 2² + 13² + 45² is the sum of 3 positive squares.
2198² = 1190² + 1848² is the sum of 2 positive squares in 1 way.
2198² is the sum of 3 positive squares.
2198 is a divisor of 1871³ - 1.
2198 is palindromic in (at least) the following bases: 13, and -36.
2198 in base 13 = 1001 and consists of only the digits '0' and '1'.
2198 in base 46 = 11a and consists of only the digits '1' and 'a'.

The number 2198 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000607: Number of partitions of n into prime parts.
A001093: a(n) = n^3 + 1.
A001100: Triangle read by rows: T(n,k) = number of permutations of length n with exactly k rising or falling successions, for n >= 1, 0 <= k <= n-1.
A001158: sigma_3(n): sum of cubes of divisors of n.
A005133: Number of index n subgroups of modular group PSL_2(Z).
A007331: Fourier coefficients of E_{infinity,4}.
A032532: Integer part of decimal 'base 2 looking' numbers divided by their actual base 2 values (denominator of a(n) is n, numerator is n written in binary but read in decimal).
A075196: Table T(n,k) by antidiagonals: T(n,k) = number of partitions of n balls of k colors.
A092314: Sum of smallest parts of all partitions of n into odd parts.
A219050: Numbers n such that 3^n + 34 is prime.