A325403 Number of permutations of the multiset of prime factors of 2n whose first part is not 2.

0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 4, 0, 1, 3, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 6, 1, 0, 4, 1, 4, 4, 1, 1, 4, 1, 1, 6, 1, 1, 9, 1, 1, 1, 2, 3, 4, 1, 1, 6, 4, 1, 4, 1, 1, 8, 1, 1, 9, 0, 4, 6, 1, 1, 4, 6, 1, 5, 1, 1, 9, 1, 4, 6, 1, 1, 4, 1, 1, 8, 4, 1, 4, 1, 1, 18, 4, 1, 4, 1, 4, 1, 1, 3, 9, 4, 1, 6, 1, 1, 18

Offset: 1

Author

Gus Wiseman, May 02 2019

Keywords

• nonn

Examples

			The a(60) = 8 permutations of {2,2,2,3,5} whose first part is not 2:
  3 2 2 2 5
  3 2 2 5 2
  3 2 5 2 2
  3 5 2 2 2
  5 2 2 2 3
  5 2 2 3 2
  5 2 3 2 2
  5 3 2 2 2
		

Links

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

Crossrefs

Cf. A008480, A056239, A112798, A325327, A325362, A325364, A325367, A325390, A325392, A325407.

Programs

Mathematica

Table[Length[Select[Permutations[Flatten[Table@@@FactorInteger[2*n]]],First[#]!=2&]],{n,100}]

PARI

A008480(n) = {my(sig=factor(n)[, 2]); vecsum(sig)!/factorback(apply(k->k!, sig))}; \\ After code in A008480
A325403(n) = (A008480(n+n)-A008480(n)); \\ Antti Karttunen, Dec 06 2021

Formula

a(n) = A008480(2n) - A008480(n) = A325392(2n).

Extensions

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