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

1,30

Comments

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

a(1) = 1 by convention.

Links

Table of n, a(n) for n=1..88.

Example

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

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}]

Crossrefs

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

Sequence in context: A345047 A031264 A345045 * A304118 A319679 A364388

Adjacent sequences: A318806 A318807 A318808 * A318810 A318811 A318812

Keyword

nonn

Author

Gus Wiseman, Sep 04 2018

Status

approved