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A335125
Number of anti-run permutations of a multiset whose multiplicities are the prime indices of n.
8
1, 1, 0, 2, 0, 1, 0, 6, 2, 0, 0, 6, 0, 0, 1, 24, 0, 12, 0, 2, 0, 0, 0, 36, 2, 0, 30, 0, 0, 10, 0, 120, 0, 0, 1, 84, 0, 0, 0, 24, 0, 3, 0, 0, 38, 0, 0, 240, 2, 18, 0, 0, 0, 246, 0, 6, 0, 0, 0, 96, 0, 0, 24, 720, 0, 0, 0, 0, 0, 14, 0, 660, 0, 0, 74, 0, 1, 0, 0
OFFSET
1,4
COMMENTS
A multiset whose multiplicities are the prime indices of n (such as row n of A305936) is not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
An anti-run is a sequence with no adjacent equal parts.
EXAMPLE
The a(n) permutations for n = 2, 4, 42, 8, 30, 18:
(1) (12) (1212131) (123) (121213) (12123)
(21) (1213121) (132) (121231) (12132)
(1312121) (213) (121312) (12312)
(231) (121321) (12321)
(312) (123121) (13212)
(321) (131212) (21213)
(132121) (21231)
(212131) (21312)
(213121) (21321)
(312121) (23121)
(31212)
(32121)
MATHEMATICA
nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Table[Length[Select[Permutations[nrmptn[n]], !MatchQ[#, {___, x_, x_, ___}]&]], {n, 100}]
CROSSREFS
Positions of zeros are A335126.
Positions of nonzeros are A335127.
The version for the prime indices themselves is A335452.
Anti-run compositions are A003242.
Anti-runs are ranked by A333489.
Separable partitions are ranked by A335433.
Separable factorizations are A335434.
Inseparable partitions are ranked by A335448.
Patterns contiguously matched by compositions are A335457.
Strict permutations of prime indices are A335489.
Sequence in context: A249820 A136579 A249731 * A335022 A249732 A076694
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 01 2020
STATUS
approved