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

1,9

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A218220 A247487 A010248 * A132068 A173441 A326851

Adjacent sequences: A325400 A325401 A325402 * A325404 A325405 A325406

Keyword

nonn

Author

Gus Wiseman, May 02 2019

Extensions

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

Status

approved