A335451 Number of permutations of the prime indices of n with all equal parts contiguous and none appearing more than twice.

1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 1, 6, 1, 0, 2, 2, 2, 2, 1, 2, 2, 0, 1, 6, 1, 2, 2, 2, 1, 0, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 6, 1, 2, 2, 0, 2, 6, 1, 2, 2, 6, 1, 0, 1, 2, 2, 2, 2, 6, 1, 0, 0, 2, 1, 6, 2, 2, 2

Offset

1,6

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=1..87.

Wikipedia, Permutation pattern

Formula

a(n) = A001221(n)! if n is cubefree, otherwise 0.

Example

The a(90) = 6 permutations are (1,2,2,3), (1,3,2,2), (2,2,1,3), (2,2,3,1), (3,1,2,2), (3,2,2,1).

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[Select[Permutations[primeMS[n]], !MatchQ[#, {___, x_, __, x_, ___}]&]], {n, 100}]

Crossrefs

Separations are counted by A003242 and A335452 and ranked by A333489.

Permutations of prime indices are counted by A008480.

Unsorted prime signature is A124010. Sorted prime signature is A118914.

Permutations of prime indices with equal parts contiguous are A333175.

STC-numbers of permutations of prime indices are A333221.

(1,2,1) and (2,1,2)-avoiding permutations of prime indices are A333175.

Numbers whose prime indices are inseparable are A335448.

(1,2,1) or (2,1,2)-matching permutations of prime indices are A335460.

(1,2,1) and (2,1,2)-matching permutations of prime indices are A335462.

Strict permutations of prime indices are counted by A335489.

Cf. A056239, A056986, A112798, A181796, A335446, A335463.

Sequence in context: A263233 A300623 A087991 * A366078 A344652 A366074

Adjacent sequences: A335448 A335449 A335450 * A335452 A335453 A335454

Keyword

nonn

Author

Gus Wiseman, Jun 21 2020

Status

approved