A335489 Number of strict permutations of the prime indices of n.

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

Also the number of (1,1)-avoiding permutations of the prime indices of n.

Links

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

Wikipedia, Permutation pattern

Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid.

Formula

If n is squarefree, a(n) = A001221(n)!; otherwise a(n) = 0.

a(n != 4) = A281188(n); a(4) = 0.

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

Positions of first appearances are A002110 with 2 replaced by 4.

Permutations of prime indices are counted by A008480.

The contiguous version is A335451.

Anti-run permutations of prime indices are counted by A335452.

(1,1,1)-avoiding permutations of prime indices are counted by A335511.

Cf. A056239, A056986, A106356, A112798, A238279, A281188, A333221, A335456, A335460, A335462, A335465.

Sequence in context: A085863 A220354 A344478 * A281188 A323439 A054008

Adjacent sequences: A335486 A335487 A335488 * A335490 A335491 A335492

Keyword

nonn

Author

Gus Wiseman, Jun 19 2020

Status

approved