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