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

1,15

Links

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

Formula

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

Example

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

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}]

Prog

(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

Crossrefs

Number of times n appears in A325390.

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

Sequence in context: A249147 A260648 A127242 * A025853 A228247 A025847

Adjacent sequences: A325389 A325390 A325391 * A325393 A325394 A325395

Keyword

nonn

Author

Gus Wiseman, May 02 2019

Extensions

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

Status

approved