Monday, November 20, 2017

Number of the day: 10991

Benoit Mandelbrot was born on this day 93 years ago.

Properties of the number 10991:

10991 is a cyclic number.
10991 = 29 × 379 is semiprime and squarefree.
10991 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 10584 totatives.
10991 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 10991 results in an emirpimes.
10991 = 223 + 73 is the sum of 2 positive cubes in 1 way.
10991 = 54962 - 54952 = 2042 - 1752 is the difference of 2 nonnegative squares in 2 ways.
10991 is the sum of 2 positive triangular numbers.
10991 is the difference of 2 positive pentagonal numbers in 2 ways.
10991 is not the sum of 3 positive squares.
109912 = 75802 + 79592 is the sum of 2 positive squares in 1 way.
109912 is the sum of 3 positive squares.
10991 is a proper divisor of 15673 - 1.
10991 is an emirpimes in (at least) the following bases: 2, 4, 8, 10, 11, 15, 17, 18, 19, 20, 22, 25, 27, 31, 32, 41, 43, 46, 47, 49, 54, 61, 65, 67, 68, 74, 76, 77, 80, 81, 82, 84, 85, 87, 90, 91, 97, 99, and 100.
10991 is palindromic in (at least) the following bases: 23, 34, -9, -67, and -99.
10991 in base 4 = 2223233 and consists of only the digits '2' and '3'.
10991 in base 23 = khk and consists of only the digits 'h' and 'k'.
10991 in base 27 = f22 and consists of only the digits '2' and 'f'.
10991 in base 34 = 9h9 and consists of only the digits '9' and 'h'.
10991 in base 60 = 33B and consists of only the digits '3' and 'B'.

The number 10991 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023192: Conjecturally, number of infinitely-recurring prime patterns on n consecutive integers.
A028948: An "extremely strange sequence": a(n+1) = [ A*a(n)+B ]/p^r, where p^r is the highest power of p diving [ A*a(n)+B ] and p=2, A=4.001, B=1.2.
A060354: The n-th n-gonal number.
A066831: Numbers n such that sigma(n) divides sigma(phi(n)).
A067383: Numbers n such that sigma(phi(n))/sigma(n) = 3.
A085366: Semiprimes that are the sum of two positive cubes. Common terms of A003325 and A046315.
A224483: Numbers which are the sum of two positive cubes and divisible by 29.
A252039: T(n,k)=Number of (n+2)X(k+2) 0..4 arrays with every 3X3 subblock row and column sum nonprime and every diagonal and antidiagonal sum prime
A255187: 29-gonal numbers: a(n) = n*(27*n-25)/2.
A262909: a(n) = greatest k such that A155043(k+A262509(n)) < A155043(A262509(n)).

Sunday, November 19, 2017

Number of the day: 15987776874

Properties of the number 15987776874:

15987776874 = 2 × 3 × 97 × 27470407 is composite and squarefree.
15987776874 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 5274317952 totatives.
15987776874 has a semiprime digit sum 69 in base 10.
15987776874 = 11922 + 21432 + 1264192 is the sum of 3 positive squares.
159877768742 = 107134587302 + 118672158242 is the sum of 2 positive squares in 1 way.
159877768742 is the sum of 3 positive squares.
15987776874 is a proper divisor of 1939156802 - 1.
15987776874 = '1598' + '7776874' is the concatenation of 2 sphenic numbers.

Saturday, November 18, 2017

Number of the day: 879706944

Properties of the number 879706944:

879706944 = 26 × 32 × 23 × 66403 is the 834681825th composite number and is not squarefree.
879706944 has 4 distinct prime factors, 84 divisors, 31 antidivisors and 280482048 totatives.
879706944 is the difference of 2 nonnegative squares in 30 ways.
879706944 is the sum of 2 positive triangular numbers.
879706944 is the difference of 2 positive pentagonal numbers in 2 ways.
879706944 = 28002 + 48882 + 291202 is the sum of 3 positive squares.
8797069442 is the sum of 3 positive squares.
879706944 is a proper divisor of 2714092 - 1.

Thursday, November 16, 2017

Number of the day: 68956

Properties of the number 68956:

68956 = 22 × 17239 is the 62103th composite number and is not squarefree.
68956 has 2 distinct prime factors, 6 divisors, 3 antidivisors and 34476 totatives.
68956 has a semiprime digit sum 34 in base 10.
68956 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 68956 results in a semiprime.
68956 = 23 + 33 + 413 is the sum of 3 positive cubes in 1 way.
68956 = 172402 - 172382 is the difference of 2 nonnegative squares in 1 way.
68956 is the difference of 2 positive pentagonal numbers in 1 way.
68956 is not the sum of 3 positive squares.
689562 is the sum of 3 positive squares.
68956 is a proper divisor of 50917 - 1.
68956 in base 51 = QQ4 and consists of only the digits '4' and 'Q'.

The number 68956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A032375: Numbers n such that 51*2^n+1 is prime.
A184642: Number of partitions of n having no parts with multiplicity 7.

Wednesday, November 15, 2017

Number of the day: 5471

Properties of the number 5471:

5471 is a cyclic number.
5471 is the 722th prime.
5471 has 9 antidivisors and 5470 totatives.
5471 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 5471 results in a semiprime.
5471 = 27362 - 27352 is the difference of 2 nonnegative squares in 1 way.
5471 is the difference of 2 positive pentagonal numbers in 1 way.
5471 is not the sum of 3 positive squares.
54712 is the sum of 3 positive squares.
5471 is a proper divisor of 2547 - 1.
5471 is an emirp in (at least) the following bases: 3, 5, 7, 9, 11, 13, 14, 16, 19, 20, 32, 33, 41, 49, 51, 55, 56, 57, 59, 61, 62, 64, 65, 66, 68, 69, 74, 77, 81, 83, 85, 86, 87, 91, 93, and 98.
5471 is palindromic in (at least) base -18.
5471 in base 3 = 21111122 and consists of only the digits '1' and '2'.
5471 in base 4 = 1111133 and consists of only the digits '1' and '3'.
5471 in base 20 = ddb and consists of only the digits 'b' and 'd'.

The number 5471 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000945: Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).
A049438: p, p+6 and p+8 are all primes (A046138) but p+2 is not.
A059802: Numbers n such that 5^n - 4^n is prime.
A078853: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d = 2, 4 or 6) and forming d-pattern=[6,2,4]; short d-string notation of pattern = [624].
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.
A136073: Father primes of order 4.
A167054: Values of A167053(k)-A167053(k-1)-1 not equal to 1.
A213978: Number of solid standard Young tableaux of shape [[n,n,n],[n]].
A214722: Number A(n,k) of solid standard Young tableaux of shape [[{n}^k],[n]]; square array A(n,k), n>=0, k>=1, read by antidiagonals.
A250755: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction

Tuesday, November 14, 2017

Number of the day: 8049637

Properties of the number 8049637:

8049637 is a cyclic number.
8049637 = 73 × 110269 is semiprime and squarefree.
8049637 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 7939296 totatives.
8049637 has an emirp digit sum 37 in base 10.
8049637 = 40248192 - 40248182 = 551712 - 550982 is the difference of 2 nonnegative squares in 2 ways.
8049637 is the sum of 2 positive triangular numbers.
8049637 is the difference of 2 positive pentagonal numbers in 2 ways.
8049637 = 12862 + 25292 = 6942 + 27512 is the sum of 2 positive squares in 2 ways.
8049637 = 1002 + 2312 + 28262 is the sum of 3 positive squares.
80496372 = 52929122 + 60647952 = 47420452 + 65045882 = 38183882 + 70863652 = 17826602 + 78497632 is the sum of 2 positive squares in 4 ways.
80496372 is the sum of 3 positive squares.
8049637 is a proper divisor of 15973063 - 1.
8049637 is an emirpimes in (at least) the following bases: 3, 5, 12, 13, 14, 15, 16, 17, 20, 21, 29, 31, 38, 41, 44, 49, 51, 55, 60, 61, 62, 71, 78, 83, 88, 93, 94, 95, and 99.

Monday, November 13, 2017

Number of the day: 6674

Properties of the number 6674:

6674 = 2 × 47 × 71 is a sphenic number and squarefree.
6674 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 3220 totatives.
6674 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 6674 results in a semiprime.
6674 is the difference of 2 positive pentagonal numbers in 1 way.
6674 = 72 + 82 + 812 is the sum of 3 positive squares.
66742 is the sum of 3 positive squares.
6674 is a proper divisor of 2832 - 1.
6674 = '6' + '674' is the concatenation of 2 semiprime numbers.
6674 is palindromic in (at least) the following bases: 48, 93, -39, and -46.
6674 in base 36 = 55e and consists of only the digits '5' and 'e'.
6674 in base 48 = 2h2 and consists of only the digits '2' and 'h'.

The number 6674 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A137094: Numbers n such that n and the square of n use only the digits 2, 4, 5, 6 and 7.
A137380: Number of primes between (Prime[n + 1])^Pi and (Prime[n])^Pi.
A138563: Beastly fax numbers: numbers containing the fax number of the Beast (667, one more than its regular number) in their decimal expansion.
A186668: Total number of n-digit numbers requiring 11 positive biquadrates in their representation as sum of biquadrates.
A208923: Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.
A229014: Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.
A252213: Number of (n+2)X(2+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A252216: Number of (n+2)X(5+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A252219: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 2 5 6 or 7
A260370: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00001111