Saturday, August 8, 2020

Number of the day: 6134

Properties of the number 6134:

6134 = 2 × 3067 is semiprime and squarefree.
6134 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 3066 totatives.
6134 has a semiprime digit sum 14 in base 10.
6134 has an oblong digit product 72 in base 10.
6134 = 52 + 222 + 752 is the sum of 3 positive squares.
61342 is the sum of 3 positive squares.
6134 is a proper divisor of 8237 - 1.
6134 = '6' + '134' is the concatenation of 2 semiprime numbers.
6134 is an emirpimes in (at least) the following bases: 4, 7, 8, 9, 16, 18, 21, 24, 26, 28, 29, 31, 39, 40, 49, 50, 52, 55, 56, 68, 74, 78, 79, 85, 86, 87, 94, and 99.
6134 is palindromic in (at least) the following bases: 19, 25, and -73.
6134 in base 6 = 44222 and consists of only the digits '2' and '4'.
6134 in base 19 = gig and consists of only the digits 'g' and 'i'.
6134 in base 25 = 9k9 and consists of only the digits '9' and 'k'.

The number 6134 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058787: Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n faces and k vertices, where (n/2+2) <= k <= (2n+8).
A058788: Triangle T(n,k) = number of polyhedra (triconnected planar graphs) with n edges and k vertices (or k faces), where (n/3+2) <= k <= (2n/3). Note that there is no such k when n=7.
A100363: Numbers n such that the numbers of divisors of n,n+1 and n+2 are k,2k,4k respectively for some k.
A122370: Dimension of 6-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 6 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( xi w ) = w and d_{xi} ( xj w ) = 0 for i/=j).
A167121: a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.
A173724: Number of reduced, normalized 3x3 semimagic squares with distinct nonnegative integer entries and maximum entry n.
A212438: Irregular triangle read by rows: T(n,k) (n >= 4, k=4..2n-4) = number of polyhedra with n faces and k vertices.
A240733: Floor(6^n/(2+2*cos(Pi/9))^n).
A317222: T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
A318683: Number of ways to split a strict integer partition of n into consecutive subsequences with equal sums.

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