This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335487 #11 Jun 30 2020 09:55:35
%S A335487 0,0,0,1,0,0,0,1,1,0,0,3,0,0,0,1,0,3,0,3,0,0,0,4,1,0,1,3,0,0,0,1,0,0,
%T A335487 0,6,0,0,0,4,0,0,0,3,3,0,0,5,1,3,0,3,0,4,0,4,0,0,0,12,0,0,3,1,0,0,0,3,
%U A335487 0,0,0,10,0,0,3,3,0,0,0,5,1,0,0,12,0,0
%N A335487 Number of (1,1)-matching permutations of the prime indices of n.
%C A335487 Depends only on sorted prime signature (A118914).
%C A335487 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.
%C A335487 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).
%H A335487 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335487 Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%F A335487 a(n) = 0 if n is squarefree, otherwise a(n) = A008480(n).
%F A335487 a(n) = A008480(n) - A281188(n) for n != 4.
%e A335487 The a(n) permutations for n = 4, 12, 24, 48, 36, 72, 60:
%e A335487 (11) (112) (1112) (11112) (1122) (11122) (1123)
%e A335487 (121) (1121) (11121) (1212) (11212) (1132)
%e A335487 (211) (1211) (11211) (1221) (11221) (1213)
%e A335487 (2111) (12111) (2112) (12112) (1231)
%e A335487 (21111) (2121) (12121) (1312)
%e A335487 (2211) (12211) (1321)
%e A335487 (21112) (2113)
%e A335487 (21121) (2131)
%e A335487 (21211) (2311)
%e A335487 (22111) (3112)
%e A335487 (3121)
%e A335487 (3211)
%t A335487 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A335487 Table[Length[Select[Permutations[primeMS[n]],!UnsameQ@@#&]],{n,100}]
%Y A335487 Positions of zeros are A005117 (squarefree numbers).
%Y A335487 The case where the match must be contiguous is A333175.
%Y A335487 The avoiding version is A335489.
%Y A335487 The (1,1,1)-matching case is A335510.
%Y A335487 Patterns are counted by A000670.
%Y A335487 Permutations of prime indices are counted by A008480.
%Y A335487 (1,1)-matching patterns are counted by A019472.
%Y A335487 (1,1)-matching compositions are counted by A261982.
%Y A335487 STC-numbers of permutations of prime indices are A333221.
%Y A335487 Patterns matched by standard compositions are counted by A335454.
%Y A335487 Dimensions of downsets of standard compositions are A335465.
%Y A335487 (1,1)-matching compositions are ranked by A335488.
%Y A335487 Cf. A000961, A056239, A056986, A112798, A181796, A335451, A335452, A335460, A335462.
%K A335487 nonn
%O A335487 1,12
%A A335487 _Gus Wiseman_, Jun 14 2020