A325392 Number of permutations of the multiset of prime factors of n whose first part is not 2.

1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 0, 2, 1, 2, 3, 1, 1, 2, 1, 1, 4, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 1, 2, 1, 1, 6, 1, 1, 3, 0, 2, 4, 1, 1, 2, 4, 1, 4, 1, 1, 3, 1, 2, 4, 1, 1, 1, 1, 1, 6, 2, 1, 2, 1, 1, 9, 2, 1, 2, 1, 2, 1, 1, 2, 3, 3, 1, 4, 1, 1, 6

Offset: 1

Author

Gus Wiseman, May 02 2019

Keywords

• nonn

Examples

			The a(90) = 9 permutations of {2,3,3,5} not starting with 2:
  3 2 3 5
  3 2 5 3
  3 3 2 5
  3 3 5 2
  3 5 2 3
  3 5 3 2
  5 2 3 3
  5 3 2 3
  5 3 3 2
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Number of times n appears in A325390.

Cf. A008480, A056239, A112798, A325327, A325362, A325364, A325367, A325403 (even bisection), A325407, A325460, A325461.

Programs

Mathematica

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

PARI

A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ From code in A008480
A325392(n) = if(n%2, A008480(n), A008480(n)-A008480(n/2)); \\ Antti Karttunen, Dec 06 2021

Formula

If n is odd, a(n) = A008480(n). If n is even, a(n) = A008480(n) - A008480(n/2).

Extensions

Data section extended up to 105 terms by Antti Karttunen, Dec 06 2021