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 A344652 #7 Jun 18 2021 01:15:32
%S A344652 1,1,1,1,1,2,1,0,1,2,1,2,1,2,2,0,1,2,1,2,2,2,1,1,1,2,0,2,1,5,1,0,2,2,
%T A344652 2,3,1,2,2,1,1,5,1,2,2,2,1,0,1,2,2,2,1,1,2,1,2,2,1,7,1,2,2,0,2,5,1,2,
%U A344652 2,5,1,2,1,2,2,2,2,5,1,0,0,2,1,7,2,2,2
%N A344652 Number of permutations of the prime indices of n with no adjacent triples (..., x, y, z, ...) such that x <= y <= z.
%C A344652 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.
%e A344652 The permutations for n = 2, 6, 8, 30, 36, 60, 180, 210, 360:
%e A344652 (1) (12) (132) (1212) (1213) (12132) (1324) (121213)
%e A344652 (21) (213) (2121) (1312) (13212) (1423) (121312)
%e A344652 (231) (2211) (1321) (13221) (1432) (121321)
%e A344652 (312) (2131) (21213) (2143) (131212)
%e A344652 (321) (2311) (21312) (2314) (132121)
%e A344652 (3121) (21321) (2413) (132211)
%e A344652 (3211) (22131) (2431) (212131)
%e A344652 (23121) (3142) (213121)
%e A344652 (23211) (3214) (213211)
%e A344652 (31212) (3241) (221311)
%e A344652 (32121) (3412) (231211)
%e A344652 (32211) (3421) (312121)
%e A344652 (4132) (321211)
%e A344652 (4213)
%e A344652 (4231)
%e A344652 (4312)
%e A344652 (4321)
%t A344652 Table[Length[Select[Permutations[Flatten[ ConstantArray@@@FactorInteger[n]]],!MatchQ[#,{___,x_,y_,z_,___}/;x<=y<=z]&]],{n,100}]
%Y A344652 All permutations of prime indices are counted by A008480.
%Y A344652 The case of permutations is A049774.
%Y A344652 Avoiding (3,2,1) also gives A344606.
%Y A344652 The wiggly case is A345164.
%Y A344652 A001250 counts wiggly permutations.
%Y A344652 A025047 counts wiggly compositions (ascend: A025048, descend: A025049).
%Y A344652 A056239 adds up prime indices, row sums of A112798.
%Y A344652 A325534 counts separable partitions, ranked by A335433.
%Y A344652 A325535 counts inseparable partitions, ranked by A335448.
%Y A344652 A335452 counts anti-run permutations of prime indices.
%Y A344652 A345170 counts partitions with a wiggly permutation, ranked by A345172.
%Y A344652 A345192 counts non-wiggly compositions, ranked by A345168.
%Y A344652 Counting compositions by patterns:
%Y A344652 - A102726 avoiding (1,2,3).
%Y A344652 - A128761 avoiding (1,2,3) adjacent.
%Y A344652 - A335514 matching (1,2,3).
%Y A344652 - A344614 avoiding (1,2,3) and (3,2,1) adjacent.
%Y A344652 - A344615 weakly avoiding (1,2,3) adjacent.
%Y A344652 Cf. A001222, A003242, A056986, A316524, A333213, A335511, A344604, A344653, A344654, A345167, A345173.
%K A344652 nonn
%O A344652 1,6
%A A344652 _Gus Wiseman_, Jun 17 2021