Friday, March 24, 2017

Number of the day: 569581

Joseph Liouville was born on this day 208 years ago.

Properties of the number 569581:

569579 and 569581 form a twin prime pair.
569581 has 5 antidivisors and 569580 totatives.
569581 has a semiprime digit sum 34 in base 10.
569581 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 569581 results in a sphenic number.
569581 = 2847912 - 2847902 is the difference of 2 nonnegative squares in 1 way.
569581 is the difference of 2 positive pentagonal numbers in 1 way.
569581 = 3552 + 6662 is the sum of 2 positive squares in 1 way.
569581 = 592 + 1742 + 7322 is the sum of 3 positive squares.
5695812 = 3175312 + 4728602 is the sum of 2 positive squares in 1 way.
5695812 is the sum of 3 positive squares.
569581 is a divisor of 10311726 - 1.
569581 is an emirp in (at least) the following bases: 9, 15, 19, 27, 48, 49, 56, 59, 61, 63, 66, 67, 71, 73, 76, 80, 81, 93, 96, and 97.

Thursday, March 23, 2017

Number of the day: 1134

Pierre-Simon Laplace was born on this day 268 years ago.

Emmy Noether was born on this day 135 years ago.

Properties of the number 1134:

1134 = 2 × 34 × 7 is the 944th composite number and is not squarefree.
1134 has 3 distinct prime factors, 20 divisors, 9 antidivisors and 324 totatives.
1134 has a semiprime digit sum 9 in base 10.
1134 has an oblong digit product 12 in base 10.
1134 is the sum of 2 positive triangular numbers.
1134 = 22 + 132 + 312 is the sum of 3 positive squares.
11342 is the sum of 3 positive squares.
1134 is a divisor of 8112 - 1.
1134 is palindromic in (at least) the following bases: 41, 53, 62, and 80.
1134 in base 33 = 11c and consists of only the digits '1' and 'c'.

The number 1134 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000969: G.f.: (1+x+2*x^2)/((1-x)^2*(1-x^3)).
A001158: sigma_3(n): sum of cubes of divisors of n.
A008290: Triangle T(n,k) of rencontres numbers (number of permutations of n elements with k fixed points).
A033485: a(n) = a(n-1) + a(floor(n/2)), a(1) = 1.
A045943: Triangular matchstick numbers: 3*n*(n+1)/2.
A046306: Numbers that are divisible by exactly 6 primes with multiplicity.
A057809: Numbers n such that pi(n) divides n.
A085787: Generalized heptagonal numbers: n*(5*n-3)/2, n=0, +-1, +-2 +-3, ...
A094159: 3 times hexagonal numbers: a(n) = 3*n*(2*n-1).
A179644: Product of the 4th power of a prime and 2 different distinct primes (p^4*q*r).

Wednesday, March 22, 2017

Number of the day: 9912

Properties of the number 9912:

9912 = 23 × 3 × 7 × 59 is the 8689th composite number and is not squarefree.
9912 has 4 distinct prime factors, 32 divisors, 19 antidivisors and 2784 totatives.
9912 has a semiprime digit sum 21 in base 10.
9912 has a Fibonacci digit sum 21 in base 10.
9912 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 9912 results in a semiprime.
9912 = 24792 - 24772 = 12412 - 12372 = 8292 - 8232 = 4192 - 4072 = 3612 - 3472 = 1912 - 1632 = 1392 - 972 = 1012 - 172 is the difference of 2 nonnegative squares in 8 ways.
9912 is the difference of 2 positive pentagonal numbers in 3 ways.
9912 = 202 + 262 + 942 is the sum of 3 positive squares.
99122 is the sum of 3 positive squares.
9912 is a divisor of 8272 - 1.
9912 = '991' + '2' is the concatenation of 2 prime numbers.
9912 is palindromic in (at least) base 39.
9912 in base 38 = 6WW and consists of only the digits '6' and 'W'.
9912 in base 39 = 6K6 and consists of only the digits '6' and 'K'.
9912 in base 44 = 55C and consists of only the digits '5' and 'C'.

The number 9912 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002597: Number of partitions into one kind of 1's, two kinds of 2's, and three kinds of 3's.
A006967: Number of graceful permutations of length n.
A025231: a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 3.
A047891: Number of planar rooted trees with n nodes and tricolored end nodes.
A049374: A triangle of numbers related to triangle A030527.
A092000: Numbers that can be expressed as the difference of the squares of primes in exactly four distinct ways.
A105720: Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.
A180281: Triangle read by rows: T(n,k) = number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to k.
A235047: Permutation of nonnegative integers: a(n) = A235199(A234840(n+1)-1).
A241648: Numbers m such that the GCD of the x's that satisfy sigma(x)=m is 3.

Tuesday, March 21, 2017

Number of the day: 1537116005136

Joseph Fourier was born on this day 249 years ago.

George David Birkhoff was born on this day 133 years ago.

Properties of the number 1537116005136:

1537116005136 = 24 × 3 × 73 × 438674659 is composite and not squarefree.
1537116005136 has 4 distinct prime factors, 40 divisors, 35 antidivisors and 505353206016 totatives.
1537116005136 has an emirpimes digit sum 39 in base 10.
1537116005136 is the difference of 2 nonnegative squares in 12 ways.
1537116005136 is the difference of 2 positive pentagonal numbers in 2 ways.
1537116005136 = 29842 + 167562 + 12396882 is the sum of 3 positive squares.
15371160051362 = 10107064143362 + 11581010997602 is the sum of 2 positive squares in 1 way.
15371160051362 is the sum of 3 positive squares.
1537116005136 is a divisor of 439146224886 - 1.
1537116005136 = '153711600513' + '6' is the concatenation of 2 semiprime numbers.

Monday, March 20, 2017

Number of the day: 689804

Properties of the number 689804:

689804 = 22 × 331 × 521 is the 634008th composite number and is not squarefree.
689804 has 3 distinct prime factors, 12 divisors, 39 antidivisors and 343200 totatives.
689804 has a semiprime digit sum 35 in base 10.
689804 = 1724522 - 1724502 = 8522 - 1902 is the difference of 2 nonnegative squares in 2 ways.
689804 is the difference of 2 positive pentagonal numbers in 2 ways.
689804 = 22 + 302 + 8302 is the sum of 3 positive squares.
6898042 = 3693962 + 5825602 is the sum of 2 positive squares in 1 way.
6898042 is the sum of 3 positive squares.
689804 is a divisor of 1667110 - 1.
689804 is palindromic in (at least) base -99.

Sunday, March 19, 2017

Number of the day: 282

Properties of the number 282:

282 = 2 × 3 × 47 is a sphenic number and squarefree.
282 has 3 distinct prime factors, 8 divisors, 5 antidivisors and 92 totatives.
282 has an oblong digit sum 12 in base 10.
282 = (3 × 4)/2 + … + (11 × 12)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
282 is the sum of 2 positive triangular numbers.
282 is the difference of 2 positive pentagonal numbers in 2 ways.
282 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
282 = 72 + 82 + 132 is the sum of 3 positive squares.
2822 is the sum of 3 positive squares.
282 is a divisor of 2812 - 1.
282 is a palindrome (in base 10).
282 is palindromic in (at least) the following bases: 5, 9, 46, 93, and -14.
282 in base 3 = 101110 and consists of only the digits '0' and '1'.
282 in base 5 = 2112 and consists of only the digits '1' and '2'.
282 in base 7 = 552 and consists of only the digits '2' and '5'.
282 in base 9 = 343 and consists of only the digits '3' and '4'.
282 consists of only the digits '2' and '8'.
282 in base 16 = 11a and consists of only the digits '1' and 'a'.

The number 282 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000219: Number of planar partitions of n.
A002113: Palindromes in base 10.
A002445: Denominators of Bernoulli numbers B_{2n}.
A002858: Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.
A005836: Numbers n whose base 3 representation contains no 2.
A007304: Sphenic numbers: products of 3 distinct primes.
A008864: a(n) = prime(n) + 1.
A014574: Average of twin prime pairs.
A024675: Average of two consecutive odd primes.
A027642: Denominator of Bernoulli number B_n.

Saturday, March 18, 2017

Number of the day: 99300

Christian Goldbach was born on this day 327 years ago.

Properties of the number 99300:

99300 = 22 × 3 × 52 × 331 is the 89767th composite number and is not squarefree.
99300 has 4 distinct prime factors, 36 divisors, 13 antidivisors and 26400 totatives.
99300 has a semiprime digit sum 21 in base 10.
99300 has a Fibonacci digit sum 21 in base 10.
99300 has a triangular digit sum 21 in base 10.
99300 = 248262 - 248242 = 82782 - 82722 = 49702 - 49602 = 16702 - 16402 = 10182 - 9682 = 4062 - 2562 is the difference of 2 nonnegative squares in 6 ways.
99300 is the difference of 2 positive pentagonal numbers in 3 ways.
99300 = 442 + 502 + 3082 is the sum of 3 positive squares.
993002 = 595802 + 794402 = 278042 + 953282 is the sum of 2 positive squares in 2 ways.
993002 is the sum of 3 positive squares.
99300 is a divisor of 18110 - 1.
99300 is palindromic in (at least) base 29.
99300 in base 29 = 4224 and consists of only the digits '2' and '4'.
99300 in base 47 = iia and consists of only the digits 'a' and 'i'.