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 A335451 Number of permutations of the prime indices of n with all equal parts contiguous and none appearing more than twice. 16
 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 1, 6, 1, 0, 2, 2, 2, 2, 1, 2, 2, 0, 1, 6, 1, 2, 2, 2, 1, 0, 1, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 6, 1, 2, 2, 0, 2, 6, 1, 2, 2, 6, 1, 0, 1, 2, 2, 2, 2, 6, 1, 0, 0, 2, 1, 6, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. LINKS Wikipedia, Permutation pattern FORMULA a(n) = A001221(n)!  if n is cubefree, otherwise 0. EXAMPLE The a(90) = 6 permutations are (1,2,2,3), (1,3,2,2), (2,2,1,3), (2,2,3,1), (3,1,2,2), (3,2,2,1). MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Table[Length[Select[Permutations[primeMS[n]], !MatchQ[#, {___, x_, __, x_, ___}]&]], {n, 100}] CROSSREFS Separations are counted by A003242 and A335452 and ranked by A333489. Permutations of prime indices are counted by A008480. Unsorted prime signature is A124010. Sorted prime signature is A118914. Permutations of prime indices with equal parts contiguous are A333175. STC-numbers of permutations of prime indices are A333221. (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A333175. Numbers whose prime indices are inseparable are A335448. (1,2,1) or (2,1,2)-matching permutations of prime indices are A335460. (1,2,1) and (2,1,2)-matching permutations of prime indices are A335462. Strict permutations of prime indices are counted by A335489. Cf. A056239, A056986, A112798, A181796, A335446, A335463. Sequence in context: A263233 A300623 A087991 * A344652 A293439 A144095 Adjacent sequences:  A335448 A335449 A335450 * A335452 A335453 A335454 KEYWORD nonn AUTHOR Gus Wiseman, Jun 21 2020 STATUS approved

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Last modified September 24 11:51 EDT 2021. Contains 347642 sequences. (Running on oeis4.)