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 A335450 Number of (2,1,2)-avoiding permutations of the prime indices of n. 6
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 1, 3, 1, 6, 1, 1, 2, 2, 2, 3, 1, 2, 2, 4, 1, 6, 1, 3, 3, 2, 1, 5, 1, 2, 2, 3, 1, 2, 2, 4, 2, 2, 1, 12, 1, 2, 3, 1, 2, 6, 1, 3, 2, 6, 1, 4, 1, 2, 2, 3, 2, 6, 1, 5, 1, 2, 1, 12, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Depends only on unsorted prime signature (A124010), but not only on sorted prime signature (A118914). 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. We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1). LINKS Wikipedia, Permutation pattern EXAMPLE The permutations for n = 2, 6, 12, 24, 30, 48, 60, 90:   (1)  (12)  (112)  (1112)  (123)  (11112)  (1123)  (1223)        (21)  (211)  (2111)  (132)  (21111)  (1132)  (1322)                             (213)           (2113)  (2123)                             (231)           (2311)  (2213)                             (312)           (3112)  (2231)                             (321)           (3211)  (3122)                                                     (3212)                                                     (3221) MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Table[Length[Select[Permutations[primeMS[n]], !MatchQ[#, {___, x_, ___, y_, ___, x_, ___}/; x>y]&]], {n, 100}] CROSSREFS Positions of ones are A000961. Replacing (2,1,2) with (1,2,1) gives A335449. The matching version is A335453. Patterns are counted by A000670. (2,1,2)-avoiding patterns are counted by A001710. Permutations of prime indices are counted by A008480. Unsorted prime signature is A124010. Sorted prime signature is A118914. (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A333175. STC-numbers of permutations of prime indices are A333221. (1,2,1) and (2,1,2)-avoiding permutations of prime indices are A335448. Patterns matched by standard compositions are counted by A335454. (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. Dimensions of downsets of standard compositions are A335465. (2,1,2)-avoiding compositions are ranked by A335469. (2,1,2)-avoiding compositions are counted by A335473. (2,2,1)-avoiding compositions are ranked by A335524. (1,2,2)-avoiding compositions are ranked by A335525. Cf. A056239, A056986, A112798, A158005, A181796, A335452, A335463. Sequence in context: A330757 A322373 A332288 * A324191 A238946 A326516 Adjacent sequences:  A335447 A335448 A335449 * A335451 A335452 A335453 KEYWORD nonn AUTHOR Gus Wiseman, Jun 14 2020 STATUS approved

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Last modified September 18 22:34 EDT 2021. Contains 347548 sequences. (Running on oeis4.)