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 A335449 Number of (1,2,1)-avoiding permutations of the prime indices of n. 7
 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 6, 1, 1, 2, 2, 2, 3, 1, 2, 2, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 3, 2, 2, 1, 4, 2, 2, 2, 2, 1, 6, 1, 2, 2, 1, 2, 6, 1, 2, 2, 6, 1, 3, 1, 2, 3, 2, 2, 6, 1, 2, 1, 2, 1, 6, 2, 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 a(n) permutations for n = 2, 10, 36, 54, 324, 30, 1458, 90:   (1)  (13)  (1122)  (1222)  (112222)  (123)  (1222222)  (1223)        (31)  (2112)  (2122)  (211222)  (132)  (2122222)  (1322)              (2211)  (2212)  (221122)  (213)  (2212222)  (2123)                      (2221)  (222112)  (231)  (2221222)  (2213)                              (222211)  (312)  (2222122)  (2231)                                        (321)  (2222212)  (3122)                                               (2222221)  (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

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)