A318809 Number of necklace permutations of the multiset of prime indices of n > 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Sep 04 2018

Keywords

• nonn

Comments

A necklace is a finite sequence that is minimal among its cyclic permutations.

a(1) = 1 by convention.

Examples

			The a(144) = 3 necklace permutations of {1,1,1,1,2,2} are: (111122), (111212), (112112).
		

Crossrefs

Cf. A000670, A000740, A008480, A008965, A056239, A059966, A112798, A298941, A318810.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
neckQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And];
Table[Length[Select[Permutations[primeMS[n]],neckQ]],{n,2,200}]