Number of the day: 733509

Pierre Joseph Louis Fatou was born on this day 141 years ago.

Properties of the number 733509:

733509 = 3³ × 7 × 3881 is the 674464^th composite number and is not squarefree.
733509 has 3 distinct prime factors, 16 divisors, 17 antidivisors and 419040 totatives.
733509 = 366755² - 366754² = 122253² - 122250² = 52397² - 52390² = 40755² - 40746² = 17475² - 17454² = 13597² - 13570² = 5853² - 5790² = 2035² - 1846² is the difference of 2 nonnegative squares in 8 ways.
733509 is the difference of 2 positive pentagonal numbers in 2 ways.
733509 = 17² + 22² + 856² is the sum of 3 positive squares.
733509² = 446040² + 582309² is the sum of 2 positive squares in 1 way.
733509² is the sum of 3 positive squares.
733509 is a proper divisor of 197¹² - 1.
733509 = '733' + '509' is the concatenation of 2 prime numbers.
733509 is palindromic in (at least) base -98.

Number of the day: 7851

Luitzen Egbertus Jan Brouwer was born on this day 138 years ago.

Properties of the number 7851:

7851 = 3 × 2617 is semiprime and squarefree.
7851 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 5232 totatives.
7851 has a semiprime digit sum 21 in base 10.
7851 has a Fibonacci digit sum 21 in base 10.
7851 has a triangular digit sum 21 in base 10.
7851 = 3926² - 3925² = 1310² - 1307² is the difference of 2 nonnegative squares in 2 ways.
7851 is the difference of 2 positive pentagonal numbers in 1 way.
7851 = 1² + 25² + 85² is the sum of 3 positive squares.
7851² = 1224² + 7755² is the sum of 2 positive squares in 1 way.
7851² is the sum of 3 positive squares.
7851 is a proper divisor of 1553⁶ - 1.
7851 is an emirpimes in (at least) the following bases: 3, 5, 8, 11, 15, 18, 20, 24, 30, 35, 37, 51, 53, 59, 63, 66, 67, 68, 69, 70, 73, 74, 78, 82, 85, 89, 90, 91, 93, and 97.
7851 is palindromic in (at least) the following bases: 31, and -21.
7851 in base 29 = 99l and consists of only the digits '9' and 'l'.
7851 in base 30 = 8ll and consists of only the digits '8' and 'l'.
7851 in base 31 = 858 and consists of only the digits '5' and '8'.
7851 in base 62 = 22d and consists of only the digits '2' and 'd'.

The number 7851 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A063052: Integers n > 879 such that the 'Reverse and Add!' trajectory of n joins the trajectory of 879.
A084449: Positions of sevens (ground states) in A084451.
A120006: Expansion of ((eta(q^2) * eta(q^14)) / (eta(q) * eta(q^7)))^3 in powers of q.
A123648: Expansion of eta(q^4) * eta(q^28) / (eta(q) * eta(q^7)) in powers of q.
A125522: A 4 x 4 permutation-free magic square.
A127873: a(n) = (n^3)/2 + (3*n^2)/2 + 3*n + 3.
A145169: G.f. A(x) satisfies A(x/A(x)^2) = 1/(1-x)^3.
A231710: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no element having a strict majority of its horizontal, vertical and antidiagonal neighbors equal to one
A240209: Number of partitions p of n such that median(p) = multiplicity(max(p)).
A240671: Floor(4^n/(2+2*cos(2*Pi/7))^n).

Number of the day: 2910297718

Properties of the number 2910297718:

2910297718 = 2 × 1455148859 is semiprime and squarefree.
2910297718 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 1455148858 totatives.
2910297718 has a semiprime digit sum 46 in base 10.
2910297718 = 43³ + 283³ + 1424³ is the sum of 3 positive cubes in 1 way.
2910297718 is the sum of 2 positive triangular numbers.
2910297718 is the difference of 2 positive pentagonal numbers in 2 ways.
2910297718 = 942² + 2177² + 53895² is the sum of 3 positive squares.
2910297718² is the sum of 3 positive squares.
2910297718 is a proper divisor of 587^9966773 - 1.
2910297718 = '29102' + '97718' is the concatenation of 2 semiprime numbers.
2910297718 is an emirpimes in (at least) the following bases: 6, 7, 13, 17, 36, 48, 51, 52, 67, 69, 70, 73, 76, 78, 80, 81, 83, 86, 87, 89, 94, and 96.

Number of the day: 12902

Properties of the number 12902:

12902 = 2 × 6451 is semiprime and squarefree.
12902 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 6450 totatives.
12902 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 12902 results in a prime.
12902 = 11² + 30² + 109² is the sum of 3 positive squares.
12902² is the sum of 3 positive squares.
12902 is a proper divisor of 131¹⁵ - 1.
12902 is an emirpimes in (at least) the following bases: 3, 4, 12, 14, 16, 21, 22, 29, 34, 39, 41, 44, 46, 47, 48, 49, 55, 58, 62, 65, 70, 72, 76, 82, 85, 87, 89, 91, 93, 96, 98, and 99.
12902 is palindromic in (at least) the following bases: 75, 97, -42, -86, and -100.
12902 in base 31 = dd6 and consists of only the digits '6' and 'd'.

The number 12902 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).
A080310: Rewrite 0->100 in the binary expansion of n (but leaving single zero as zero) and append 10 to the right.
A094659: Number of closed walks of length n at a vertex of the cyclic graph on 7 nodes C_7.
A098498: Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the edge.
A217991: Numbers n such that n^16+1 and (n+2)^16+1 are both prime.
A227135: Partitions with parts repeated at most twice and repetition only allowed if first part has an even index (first index = 1).
A270127: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled von Neumann neighborhood.
A304709: Number of integer partitions of n whose distinct parts are pairwise coprime.
A320542: a(n) is the number of ways to select 3 distinct points forming a triangle of unsigned area = n from a square of grid points with side length n, divided by 4.

Number of the day: 7852

Properties of the number 7852:

7852 = 2² × 13 × 151 is the 6860^th composite number and is not squarefree.
7852 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 3600 totatives.
7852 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 7852 results in a semiprime.
7852 = 1964² - 1962² = 164² - 138² is the difference of 2 nonnegative squares in 2 ways.
7852 is the sum of 2 positive triangular numbers.
7852 is the difference of 2 positive pentagonal numbers in 2 ways.
7852 = 6² + 54² + 70² is the sum of 3 positive squares.
7852² = 3020² + 7248² is the sum of 2 positive squares in 1 way.
7852² is the sum of 3 positive squares.
7852 is a proper divisor of 269³ - 1.
7852 is palindromic in (at least) the following bases: 12, 47, and -31.
7852 in base 11 = 5999 and consists of only the digits '5' and '9'.
7852 in base 12 = 4664 and consists of only the digits '4' and '6'.
7852 in base 20 = jcc and consists of only the digits 'c' and 'j'.
7852 in base 29 = 99m and consists of only the digits '9' and 'm'.
7852 in base 46 = 3WW and consists of only the digits '3' and 'W'.
7852 in base 47 = 3Q3 and consists of only the digits '3' and 'Q'.
7852 in base 62 = 22e and consists of only the digits '2' and 'e'.

The number 7852 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008404: Number of Costas arrays of order n, counting rotations and flips as distinct.
A029907: a(n+1) = a(n) + a(n-1) + Fibonacci(n).
A050710: Smallest composite that when added to sum of prime factors reaches a prime after n iterations.
A067563: Product of n-th prime number and n-th composite number.
A077014: Number of ways that a directed line (or river) that starts in the south can cross an east-west road n times.
A112861: Numbers n such that (2*n)!/(2*(n!)^2) - 1 is prime.
A165778: Numbers n such that |2^n-57| is prime.
A210599: Triangle of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
A271293: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 345", based on the 5-celled von Neumann neighborhood.
A299291: Coordination sequence for "ubt" 3D uniform tiling.

Number of the day: 4270

Properties of the number 4270:

4270 = 2 × 5 × 7 × 61 is the 3684^th composite number and is squarefree.
4270 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 1440 totatives.
4270 has an emirp digit sum 13 in base 10.
4270 has a Fibonacci digit sum 13 in base 10.
4270 is the difference of 2 positive pentagonal numbers in 4 ways.
4270 = 11² + 30² + 57² is the sum of 3 positive squares.
4270² = 1904² + 3822² = 770² + 4200² = 2898² + 3136² = 2562² + 3416² is the sum of 2 positive squares in 4 ways.
4270² is the sum of 3 positive squares.
4270 is a proper divisor of 1709² - 1.
4270 = '42' + '70' is the concatenation of 2 sphenic numbers.
4270 is palindromic in (at least) the following bases: 20, 26, 44, and 69.
4270 in base 11 = 3232 and consists of only the digits '2' and '3'.
4270 in base 20 = ada and consists of only the digits 'a' and 'd'.
4270 in base 25 = 6kk and consists of only the digits '6' and 'k'.
4270 in base 26 = 686 and consists of only the digits '6' and '8'.
4270 in base 43 = 2DD and consists of only the digits '2' and 'D'.
4270 in base 44 = 292 and consists of only the digits '2' and '9'.

The number 4270 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006036: Primitive pseudoperfect numbers.
A022264: a(n) = n*(7*n - 1)/2.
A050036: a(n) = a(n-1)+a(m), where m=2n-3-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A050052: a(n) = a(n-1)+a(m), where m=2n-3-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A050068: a(n) = a(n-1)+a(m), where m=2n-3-2^(p+1) and 2^p<n-1<=2^(p+1), for n >= 4.
A079641: Matrix product of Stirling2-triangle A008277(n,k) and unsigned Stirling1-triangle |A008275(n,k)|.
A104494: Positive integers n such that n^17 + 1 is semiprime (A001358).
A135036: Sums of the products of n consecutive pairs of numbers.
A141391: a(n) is the smallest unused number such that the RMS (Root Mean Square) of a(1) through a(n) is an integer.
A212964: Number of (w,x,y) with all terms in {0,...,n} and |w-x| < |x-y| < |y-w|.

Number of the day: 570452813968

Frank Plumpton Ramsey was born on this day 116 years ago.

Properties of the number 570452813968:

570452813968 = 2⁴ × 67 × 532138819 is composite and not squarefree.
570452813968 has 3 distinct prime factors, 20 divisors, 111 antidivisors and 280969295904 totatives.
570452813968 has an emirpimes digit sum 58 in base 10.
570452813968 = 142613203493² - 142613203491² = 71306601748² - 71306601744² = 35653300877² - 35653300869² = 2128555343² - 2128555209² = 1064277772² - 1064277504² = 532139087² - 532138551² is the difference of 2 nonnegative squares in 6 ways.
570452813968 is the sum of 2 positive triangular numbers.
570452813968 is the difference of 2 positive pentagonal numbers in 2 ways.
570452813968 = 12364² + 20784² + 754896² is the sum of 3 positive squares.
570452813968² is the sum of 3 positive squares.
570452813968 is a proper divisor of 89^33070774 - 1.

Number of the day: 786851

Properties of the number 786851:

786851 is a cyclic number.
786851 = 13 × 60527 is semiprime and squarefree.
786851 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 726312 totatives.
786851 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 786851 results in an emirpimes.
786851 = 8³ + 32³ + 91³ is the sum of 3 positive cubes in 1 way.
786851 = 393426² - 393425² = 30270² - 30257² is the difference of 2 nonnegative squares in 2 ways.
786851 is the difference of 2 positive pentagonal numbers in 2 ways.
786851 = 1² + 9² + 887² is the sum of 3 positive squares.
786851² = 302635² + 726324² is the sum of 2 positive squares in 1 way.
786851² is the sum of 3 positive squares.
786851 is a proper divisor of 463²²⁸⁴ - 1.
786851 = '7' + '86851' is the concatenation of 2 prime numbers.
786851 = '78' + '6851' is the concatenation of 2 sphenic numbers.
786851 is an emirpimes in (at least) the following bases: 2, 7, 8, 9, 10, 11, 15, 19, 23, 31, 35, 42, 45, 47, 48, 50, 52, 55, 58, 61, 63, 69, 70, 71, 79, 83, 92, 94, 98, and 99.
786851 is palindromic in (at least) base -97.

Number of the day: 8632860294414

Properties of the number 8632860294414:

8632860294414 = 2 × 3 × 157 × 701 × 13073317 is composite and squarefree.
8632860294414 has 5 distinct prime factors, 32 divisors, 21 antidivisors and 2855212214400 totatives.
8632860294414 has a semiprime digit sum 57 in base 10.
8632860294414 is the difference of 2 positive pentagonal numbers in 4 ways.
8632860294414 = 1658² + 2953² + 2938171² is the sum of 3 positive squares.
8632860294414² = 5429123678040² + 6711996197214² = 4219596816114² + 7531353103680² = 1125257803614² + 8559209761320² = 3687890443536² + 7805494278990² = 529797669336² + 8616588146850² = 2703872518464² + 8198496829710² = 5110466782386² + 6957686837520² = 4565952593160² + 7326551288286² = 2165357057886² + 8356883729880² = 5006975824464² + 7032529413810² = 4673841560670² + 7258201011864² = 1648414540530² + 8474019492864² = 3201916799640² + 8017107063714² is the sum of 2 positive squares in 13 ways.
8632860294414² is the sum of 3 positive squares.
8632860294414 is a proper divisor of 101^24418550 - 1.
8632860294414 = '863286029' + '4414' is the concatenation of 2 semiprime numbers.

Number of the day: 60669

Properties of the number 60669:

60669 = 3⁴ × 7 × 107 is the 54552^th composite number and is not squarefree.
60669 has 3 distinct prime factors, 20 divisors, 23 antidivisors and 34344 totatives.
60669 = 7³ + 29³ + 33³ is the sum of 3 positive cubes in 1 way.
60669 is the difference of 2 nonnegative squares in 10 ways.
60669 is the sum of 2 positive triangular numbers.
60669 is the difference of 2 positive pentagonal numbers in 1 way.
60669 = 22² + 67² + 236² is the sum of 3 positive squares.
60669² is the sum of 3 positive squares.
60669 is a proper divisor of 641⁵⁴ - 1.
60669 is palindromic in (at least) the following bases: 59, 68, and -98.
60669 in base 52 = MMb and consists of only the digits 'M' and 'b'.
60669 in base 56 = JJL and consists of only the digits 'J' and 'L'.
60669 in base 59 = HPH and consists of only the digits 'H' and 'P'.

The number 60669 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A151030: 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, -1), (0, 0, 1), (0, 1, 0), (1, 0, 1)}

Number of the day: 1848

Properties of the number 1848:

1848 = 2³ × 3 × 7 × 11 is the 1564^th composite number and is not squarefree.
1848 has 4 distinct prime factors, 32 divisors, 9 antidivisors and 480 totatives.
1848 has a semiprime digit sum 21 in base 10.
1848 has a Fibonacci digit sum 21 in base 10.
1848 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 1848 results in a sphenic number.
1848 = 463² - 461² = 233² - 229² = 157² - 151² = 83² - 71² = 73² - 59² = 53² - 31² = 47² - 19² = 43² - 1² is the difference of 2 nonnegative squares in 8 ways.
1848 is the sum of 2 positive triangular numbers.
1848 is the difference of 2 positive pentagonal numbers in 2 ways.
1848 = 2² + 20² + 38² is the sum of 3 positive squares.
1848² is the sum of 3 positive squares.
1848 is a proper divisor of 43² - 1.
1848 is palindromic in (at least) the following bases: 19, 26, 43, 55, 65, 76, 83, 87, -5, and -16.
1848 in base 15 = 833 and consists of only the digits '3' and '8'.
1848 in base 17 = 66c and consists of only the digits '6' and 'c'.
1848 in base 18 = 5cc and consists of only the digits '5' and 'c'.
1848 in base 19 = 525 and consists of only the digits '2' and '5'.
1848 in base 21 = 440 and consists of only the digits '0' and '4'.
1848 in base 25 = 2nn and consists of only the digits '2' and 'n'.
1848 in base 26 = 2j2 and consists of only the digits '2' and 'j'.

The number 1848 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000926: Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).
A005563: a(n) = n*(n+2) = (n+1)^2 - 1.
A007434: Jordan function J_2(n) (a generalization of phi(n)).
A020492: Balanced numbers: numbers n such that phi(n) (A000010) divides sigma(n) (A000203).
A033996: 8 times triangular numbers: a(n) = 4*n*(n+1).
A062354: a(n) = sigma(n)*phi(n).
A063886: Number of n-step walks on a line starting from the origin but not returning to it.
A067998: a(n) = n^2 - 2*n.
A069482: a(n) = prime(n+1)^2 - prime(n)^2.
A137932: Terms in an n X n spiral that do not lie on its principal diagonals.

Number of the day: 5077

Properties of the number 5077:

5077 is a cyclic number.
5077 is the 678^th prime.
5077 has 13 antidivisors and 5076 totatives.
5077 has a prime digit sum 19 in base 10.
5077 has sum of divisors equal to 5078 which is an emirpimes.
Reversing the decimal digits of 5077 results in a sphenic number.
5077 = 2539² - 2538² is the difference of 2 nonnegative squares in 1 way.
5077 is the difference of 2 positive pentagonal numbers in 1 way.
5077 = 6² + 71² is the sum of 2 positive squares in 1 way.
5077 = 15² + 44² + 54² is the sum of 3 positive squares.
5077² = 852² + 5005² is the sum of 2 positive squares in 1 way.
5077² is the sum of 3 positive squares.
5077 is a proper divisor of 967²⁷ - 1.
5077 is an emirp in (at least) the following bases: 3, 7, 8, 16, 33, 38, 40, 49, 51, 52, 56, 57, 58, 59, 61, 68, 69, 75, 79, 80, 81, 82, 83, 86, 91, 92, 97, and 98.
5077 is palindromic in (at least) the following bases: 26, 54, -12, -43, and -94.
5077 in base 22 = aah and consists of only the digits 'a' and 'h'.
5077 in base 26 = 7d7 and consists of only the digits '7' and 'd'.
5077 in base 53 = 1gg and consists of only the digits '1' and 'g'.
5077 in base 54 = 1e1 and consists of only the digits '1' and 'e'.

The number 5077 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045711: Primes with first digit 5.
A052049: a(n)^2 is a square whose digits occur with an equal minimum frequency of 2.
A054552: a(n) = 4*n^2 - 3*n + 1.
A075586: Primes p(k) such that the number of distinct prime divisors of all composite numbers between p(k) and p(k+1) is 6.
A128345: Numbers n such that (8^n - 5^n)/3 is prime.
A141978: Primes congruent to 2 mod 29.
A168022: Noncomposite numbers in the eastern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
A229694: T(n,k)=Number of defective 3-colorings of an nXk 0..2 array connected horizontally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order
A240130: Least prime of the form prime(n)^2 + k^2, or 0 if none.
A255027: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 or 1 and no antidiagonal sum 0 or 1 and no row sum 0 or 1 and no column sum 0 or 1

Number of the day: 25096669435

Properties of the number 25096669435:

25096669435 is a cyclic number.
25096669435 = 5 × 16363 × 306749 is a sphenic number and squarefree.
25096669435 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 20076043104 totatives.
25096669435 has a semiprime digit sum 55 in base 10.
25096669435 has a Fibonacci digit sum 55 in base 10.
25096669435 has a triangular digit sum 55 in base 10.
25096669435 = 12548334718² - 12548334717² = 2509666946² - 2509666941² = 775054² - 758691² = 194282² - 112467² is the difference of 2 nonnegative squares in 4 ways.
25096669435 is the difference of 2 positive pentagonal numbers in 3 ways.
25096669435 = 525² + 1727² + 158409² is the sum of 3 positive squares.
25096669435² = 15058001661² + 20077335548² = 4680734328² + 24656308379² = 11397271301² + 22359450432² = 11049197565² + 22533487300² is the sum of 2 positive squares in 4 ways.
25096669435² is the sum of 3 positive squares.
25096669435 is a proper divisor of 1171⁹⁵⁵⁶³⁸ - 1.

Number of the day: 231378

Galileo Galilei was born on this day 455 years ago.

Alfred North Whitehead was born on this day 158 years ago.

Properties of the number 231378:

231378 = 2 × 3 × 7² × 787 is the 210828^th composite number and is not squarefree.
231378 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 66024 totatives.
231378 is the sum of 2 positive triangular numbers.
231378 = 1² + 4² + 481² is the sum of 3 positive squares.
231378² is the sum of 3 positive squares.
231378 is a proper divisor of 379²¹ - 1.
231378 = '231' + '378' is the concatenation of 2 triangular numbers.

Number of the day: 59581315379

Properties of the number 59581315379:

59581315379 = 23 × 691 × 3748903 is a sphenic number and squarefree.
59581315379 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 56908332360 totatives.
59581315379 has an oblong digit sum 56 in base 10.
59581315379 = 29790657690² - 29790657689² = 1295245998² - 1295245975² = 43112730² - 43112039² = 1882398² - 1866505² is the difference of 2 nonnegative squares in 4 ways.
59581315379 is the difference of 2 positive pentagonal numbers in 4 ways.
59581315379 = 453² + 833² + 244091² is the sum of 3 positive squares.
59581315379² is the sum of 3 positive squares.
59581315379 is a proper divisor of 1381^3748902 - 1.
59581315379 = '595' + '81315379' is the concatenation of 2 sphenic numbers.

Number of the day: 382608

Peter Gustav Lejeune Dirichlet was born on this day 214 years ago.

Properties of the number 382608:

382608 = 2⁴ × 3² × 2657 is the 350117^th composite number and is not squarefree.
382608 has 3 distinct prime factors, 30 divisors, 13 antidivisors and 127488 totatives.
382608 is the difference of 2 nonnegative squares in 9 ways.
382608 is the difference of 2 positive pentagonal numbers in 1 way.
382608 = 192² + 588² is the sum of 2 positive squares in 1 way.
382608 = 4² + 56² + 616² is the sum of 3 positive squares.
382608² = 225792² + 308880² is the sum of 2 positive squares in 1 way.
382608² is the sum of 3 positive squares.
382608 is a proper divisor of 163⁴ - 1.
382608 is palindromic in (at least) the following bases: 97, and -95.

Number of the day: 68814649820

Properties of the number 68814649820:

68814649820 = 2² × 5 × 7 × 71 × 6923003 is composite and not squarefree.
68814649820 has 5 distinct prime factors, 48 divisors, 47 antidivisors and 23261286720 totatives.
68814649820 has an oblong digit sum 56 in base 10.
68814649820 = 17203662456² - 17203662454² = 3440732496² - 3440732486² = 2457666072² - 2457666058² = 491533248² - 491533178² = 242305176² - 242305034² = 48461376² - 48460666² = 34615512² - 34614518² = 6925488² - 6920518² is the difference of 2 nonnegative squares in 8 ways.
68814649820 is the difference of 2 positive pentagonal numbers in 8 ways.
68814649820 is not the sum of 3 positive squares.
68814649820² = 41288789892² + 55051719856² is the sum of 2 positive squares in 1 way.
68814649820² is the sum of 3 positive squares.
68814649820 is a proper divisor of 1063⁷¹⁵⁸²⁰ - 1.

Number of the day: 5449

Properties of the number 5449:

5449 is a cyclic number.
5449 is the 721^th prime.
5449 has 13 antidivisors and 5448 totatives.
5449 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 5449 results in a semiprime.
5449 = 2725² - 2724² is the difference of 2 nonnegative squares in 1 way.
5449 is the difference of 2 positive pentagonal numbers in 1 way.
5449 = 43² + 60² is the sum of 2 positive squares in 1 way.
5449 = 2² + 33² + 66² is the sum of 3 positive squares.
5449² = 1751² + 5160² is the sum of 2 positive squares in 1 way.
5449² is the sum of 3 positive squares.
5449 is a proper divisor of 17²²⁷ - 1.
5449 = '5' + '449' is the concatenation of 2 prime numbers.
5449 is an emirp in (at least) the following bases: 4, 9, 17, 20, 23, 27, 31, 45, 56, 61, 63, 65, 66, 68, 76, 79, 83, 85, and 86.
5449 is palindromic in (at least) base 19.
5449 in base 19 = f1f and consists of only the digits '1' and 'f'.
5449 in base 42 = 33V and consists of only the digits '3' and 'V'.

The number 5449 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001136: Primes p such that the multiplicative order of 2 modulo p is (p-1)/6.
A035095: Smallest prime congruent to 1 (mod prime(n)).
A061779: Primes p such that q-p = 22, where q is the next prime after p.
A066674: Least number m such that phi(m) = A000010(m) is divisible by the n-th prime.
A066739: Number of representations of n as a sum of products of positive integers. 1 is not allowed as a factor, unless it is the only factor. Representations which differ only in the order of terms or factors are considered equivalent.
A112796: Primes such that the sum of the predecessor and successor primes is divisible by 17.
A124179: Prime(R(p)) where Prime(i) is the i-th prime and R(p) is the value of the reverse of the digits of prime p.
A125878: a(n) = the least number k such that cos(2pi/k) is an algebraic number of a prime(n)-smooth degree, but not prime(n-1)-smooth.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A247981: Primes dividing nonzero terms in A003095: the iterates of x^2 + 1 starting at 0.

Number of the day: 475612

Properties of the number 475612:

475612 = 2² × 118903 is the 435946^th composite number and is not squarefree.
475612 has 2 distinct prime factors, 6 divisors, 29 antidivisors and 237804 totatives.
475612 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 475612 results in a semiprime.
475612 = 118904² - 118902² is the difference of 2 nonnegative squares in 1 way.
475612 is the difference of 2 positive pentagonal numbers in 1 way.
475612 is not the sum of 3 positive squares.
475612² is the sum of 3 positive squares.
475612 is a proper divisor of 619⁴² - 1.

Number of the day: 272019

Godfrey Harold Hardy was born on this day 142 years ago.

Happy e-Day!

Properties of the number 272019:

272019 is a cyclic number.
272019 = 3 × 11 × 8243 is a sphenic number and squarefree.
272019 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 164840 totatives.
272019 has a semiprime digit sum 21 in base 10.
272019 has a Fibonacci digit sum 21 in base 10.
272019 has a triangular digit sum 21 in base 10.
272019 = 136010² - 136009² = 45338² - 45335² = 12370² - 12359² = 4138² - 4105² is the difference of 2 nonnegative squares in 4 ways.
272019 is the sum of 2 positive triangular numbers.
272019 is the difference of 2 positive pentagonal numbers in 2 ways.
272019 = 17² + 103² + 511² is the sum of 3 positive squares.
272019² is the sum of 3 positive squares.
272019 is a proper divisor of 1103¹³⁰ - 1.
272019 = '2' + '72019' is the concatenation of 2 prime numbers.
272019 = '27201' + '9' is the concatenation of 2 semiprime numbers.
272019 is palindromic in (at least) the following bases: -18, and -89.

Number of the day: 115532808

Properties of the number 115532808:

115532808 = 2³ × 3 × 257 × 18731 is the 108931458^th composite number and is not squarefree.
115532808 has 4 distinct prime factors, 32 divisors, 35 antidivisors and 38359040 totatives.
115532808 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 115532808 results in a sphenic number.
115532808 = 28883203² - 28883201² = 14441603² - 14441599² = 9627737² - 9627731² = 4813873² - 4813861² = 112643² - 112129² = 56707² - 55679² = 38233² - 36691² = 20273² - 17189² is the difference of 2 nonnegative squares in 8 ways.
115532808 is the difference of 2 positive pentagonal numbers in 1 way.
115532808 = 208² + 430² + 10738² is the sum of 3 positive squares.
115532808² = 14385408² + 114633720² is the sum of 2 positive squares in 1 way.
115532808² is the sum of 3 positive squares.
115532808 is a proper divisor of 1301⁷⁴⁹² - 1.

Number of the day: 5629

Properties of the number 5629:

5629 is a cyclic number.
5629 = 13 × 433 is semiprime and squarefree.
5629 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 5184 totatives.
5629 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 5629 results in a sphenic number.
5629 = 2815² - 2814² = 223² - 210² is the difference of 2 nonnegative squares in 2 ways.
5629 is the difference of 2 positive pentagonal numbers in 2 ways.
5629 = 27² + 70² = 2² + 75² is the sum of 2 positive squares in 2 ways.
5629 = 2² + 45² + 60² is the sum of 3 positive squares.
5629² = 1885² + 5304² = 300² + 5621² = 3780² + 4171² = 2165² + 5196² is the sum of 2 positive squares in 4 ways.
5629² is the sum of 3 positive squares.
5629 is a proper divisor of 199⁶ - 1.
5629 = '562' + '9' is the concatenation of 2 semiprime numbers.
5629 is an emirpimes in (at least) the following bases: 3, 4, 5, 7, 8, 16, 21, 22, 25, 27, 33, 40, 42, 43, 49, 50, 51, 52, 53, 55, 56, 57, 63, 64, 69, 70, 71, 76, 77, 79, 81, 82, 85, 86, 87, 88, 89, 94, 96, and 99.
5629 is palindromic in (at least) the following bases: 67, -37, and -84.
5629 in base 4 = 1113331 and consists of only the digits '1' and '3'.
5629 in base 12 = 3311 and consists of only the digits '1' and '3'.
5629 in base 26 = 88d and consists of only the digits '8' and 'd'.
5629 in base 33 = 55j and consists of only the digits '5' and 'j'.
5629 in base 37 = 445 and consists of only the digits '4' and '5'.

The number 5629 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001210: a(n) = solution to the postage stamp problem with 5 denominations and n stamps.
A046259: a(1) = 9; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A066529: a(n) is the least index such that the least primitive root of the a(n)-th prime is n, or zero if no such prime exists.
A069833: Prefixing, suffixing or inserting a 9 in the number anywhere gives a prime.
A078370: a(n) = 4*(n+1)*n + 5.
A113340: Triangle P, read by rows, such that P^2 transforms column k of P into column k+1 of P, so that column k of P equals column 0 of P^(2*k+1), where P^2 denotes the matrix square of P.
A214393: Numbers of the form (4k+3)^2+4 or (4k+5)^2-8.
A260294: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001001
A277701: Positions of ones in A264977; positions of twos in A277330.
A299266: Coordination sequence for "cab" 3D uniform tiling formed from octahedra and truncated cubes.

Number of the day: 2479

Properties of the number 2479:

2479 is a cyclic number.
2479 = 37 × 67 is semiprime and squarefree.
2479 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 2376 totatives.
2479 has a semiprime digit sum 22 in base 10.
2479 has sum of divisors equal to 2584 which is a Fibonacci number.
Reversing the decimal digits of 2479 results in an emirpimes.
2479 = 1240² - 1239² = 52² - 15² is the difference of 2 nonnegative squares in 2 ways.
2479 is the difference of 2 positive pentagonal numbers in 2 ways.
2479 is not the sum of 3 positive squares.
2479² = 804² + 2345² is the sum of 2 positive squares in 1 way.
2479² is the sum of 3 positive squares.
2479 is a proper divisor of 269³ - 1.
2479 = '2' + '479' is the concatenation of 2 prime numbers.
2479 = '247' + '9' is the concatenation of 2 semiprime numbers.
2479 is an emirpimes in (at least) the following bases: 3, 4, 5, 9, 10, 14, 16, 17, 18, 20, 25, 27, 29, 34, 36, 37, 38, 39, 45, 49, 53, 55, 57, 61, 64, 65, 73, 74, 83, 84, 85, 86, 93, 96, 97, and 98.
2479 is palindromic in (at least) the following bases: 6, 42, 66, -25, and -59.
2479 in base 24 = 477 and consists of only the digits '4' and '7'.
2479 in base 41 = 1JJ and consists of only the digits '1' and 'J'.
2479 in base 42 = 1H1 and consists of only the digits '1' and 'H'.
2479 in base 49 = 11T and consists of only the digits '1' and 'T'.

The number 2479 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A097546: Denominators of "Farey fraction" approximations to Pi.
A113745: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 8 multiples of n-1, n-2, ..., 1, for n>=1.
A116522: a(0)=1, a(1)=1, a(n)=7a(n/2) for n=2,4,6,..., a(n)=6a((n-1)/2)+a((n+1)/2) for n=3,5,7,....
A129374: G.f. satisfies: A(x) = 1/(1-x) * A(x^2)*A(x^3)*A(x^4)*...*A(x^n)*...
A138993: a(n) = Frobenius number for 7 successive primes = F[p(n),p(n+1),p(n+2),p(n+3),p(n+4),p(n+5),p(n+6)].
A143938: The Wiener index of a benzenoid consisting of a linear chain of n hexagons.
A219051: Numbers n such that 3^n - 34 is prime.
A257751: Quasi-Carmichael numbers to exactly one base.
A257938: Least positive integer k such that prime(k*n) - 1 = (prime(i*n)-1)*(prime(j*n)-1) for some integers 0 < i < j < k.
A272412: Numbers n such that sigma(n) is a Fibonacci number.

Number of the day: 361016

Gaston Julia was born on this day 126 years ago.

Properties of the number 361016:

361016 = 2³ × 45127 is the 330187^th composite number and is not squarefree.
361016 has 2 distinct prime factors, 8 divisors, 5 antidivisors and 180504 totatives.
361016 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 361016 results in a prime.
361016 = 90255² - 90253² = 45129² - 45125² is the difference of 2 nonnegative squares in 2 ways.
361016 = 36² + 46² + 598² is the sum of 3 positive squares.
361016² is the sum of 3 positive squares.
361016 is a proper divisor of 977²³ - 1.
361016 = '36101' + '6' is the concatenation of 2 semiprime numbers.
361016 is palindromic in (at least) base 80.

Number of the day: 3137

Bartel Leendert van der Waerden was born on this day 116 years ago.

Properties of the number 3137:

3137 is a cyclic number.
3137 is the 446^th prime.
3137 has 15 antidivisors and 3136 totatives.
3137 has a semiprime digit sum 14 in base 10.
3137 has sum of divisors equal to 3138 which is a sphenic number.
Reversing the decimal digits of 3137 results in a semiprime.
3137 = 1569² - 1568² is the difference of 2 nonnegative squares in 1 way.
3137 is the difference of 2 positive pentagonal numbers in 1 way.
3137 = 1² + 56² is the sum of 2 positive squares in 1 way.
3137 = 12² + 17² + 52² is the sum of 3 positive squares.
3137² = 112² + 3135² is the sum of 2 positive squares in 1 way.
3137² is the sum of 3 positive squares.
3137 is a proper divisor of 1949⁷ - 1.
3137 = '3' + '137' is the concatenation of 2 prime numbers.
3137 is an emirp in (at least) the following bases: 2, 3, 9, 11, 13, 15, 19, 20, 24, 29, 32, 35, 42, 44, 45, 53, 54, 59, 61, 64, 65, 66, 71, 75, 76, 79, 80, 81, 84, 85, 88, 89, 91, 94, 95, and 99.
3137 is palindromic in (at least) the following bases: 33, 49, 56, -21, -27, -55, -56, -64, and -98.
3137 in base 33 = 2t2 and consists of only the digits '2' and 't'.
3137 in base 39 = 22H and consists of only the digits '2' and 'H'.
3137 in base 48 = 1HH and consists of only the digits '1' and 'H'.
3137 in base 49 = 1F1 and consists of only the digits '1' and 'F'.
3137 in base 55 = 122 and consists of only the digits '1' and '2'.
3137 in base 56 = 101 and consists of only the digits '0' and '1'.

The number 3137 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002496: Primes of the form n^2 + 1.
A014442: Largest prime factor of n^2 + 1.
A024770: Right-truncatable primes: every prefix is prime.
A033548: Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k.
A053755: a(n) = 4*n^2 + 1.
A056109: Fifth spoke of a hexagonal spiral.
A069489: Primes > 1000 in which every substring of length 3 is also prime.
A146348: Primes p such that continued fraction of (1+sqrt(p))/2 has period 3.
A211685: Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).
A215991: Primes that are the sum of 25 consecutive primes.