Wednesday, September 7, 2016

Number of the day: 1532

Properties of the number 1532:

1532 = 22 × 383 is the 1289th composite number and is not squarefree.
1532 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 764 totatives.
1532 has a prime digit sum 11 in base 10.
1532 has a sphenic digit product 30 in base 10.
1532 has an oblong digit product 30 in base 10.
Reversing the decimal digits of 1532 results in a prime.
1532 = 3842 - 3822 is the difference of 2 nonnegative squares in 1 way.
1532 is the difference of 2 positive pentagonal numbers in 1 way.
1532 is not the sum of 3 positive squares.
15322 is the sum of 3 positive squares.
1532 is a divisor of 15312 - 1.
1532 = '1' + '532' is the concatenation of 2 pentagonal numbers.
1532 is palindromic in (at least) the following bases: -30, and -34.
1532 in base 3 = 2002202 and consists of only the digits '0' and '2'.
1532 in base 5 = 22112 and consists of only the digits '1' and '2'.
1532 in base 17 = 552 and consists of only the digits '2' and '5'.
1532 in base 19 = 44c and consists of only the digits '4' and 'c'.
1532 in base 22 = 33e and consists of only the digits '3' and 'e'.
1532 in base 27 = 22k and consists of only the digits '2' and 'k'.

The number 1532 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000084: Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon.
A017817: a(0)=1, a(1)=a(2)=0, a(3)=1; a(n) = a(n-3) + a(n-4).
A058951: Coefficients of monic primitive irreducible polynomials over GF(7) listed in lexicographic order.
A097037: Initial values for iteration of A063919[x] function such that iteration ends in a 2-cycle i.e. "attracted" by unitary sociable numbers, A063991.
A161330: Snowflake (or E-toothpick) sequence (see Comments lines for definition).
A184943: Number of connected 4-regular simple graphs on n vertices with girth exactly 3.
A186733: Triangular array C(n,r) = number of connected r-regular graphs, having girth exactly 3, with n nodes, for 0 <= r < n.
A199847: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous
A217729: Trajectory of 40 under the map n-> A006369(n).
A262163: Number A(n,k) of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

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