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 A336107 #11 Sep 17 2020 20:33:07
%S A336107 0,0,0,1,0,0,0,1,1,0,0,2,0,0,0,1,0,2,0,2,0,0,0,4,1,0,1,2,0,0,0,1,0,0,
%T A336107 0,4,0,0,0,4,0,0,0,2,2,0,0,5,1,2,0,2,0,4,0,4,0,0,0,6,0,0,2,1,0,0,0,2,
%U A336107 0,0,0,9,0,0,2,2,0,0,0,5,1,0,0,6,0,0,0
%N A336107 Number of permutations of the prime indices of n with at least one non-singleton run, or non-separations.
%C A336107 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 A336107 A separation (or Carlitz composition) of a multiset is a permutation with no adjacent equal parts.
%F A336107 a(n) = A008480(n) - A335452(n).
%F A336107 a(A000961(n)) = 0 if n is in A027883, otherwise 1.
%F A336107 a(A005117(n)) = 0.
%F A336107 a(n!) = A335459(n).
%F A336107 a(A006939(n)) = A022915(n).
%e A336107 The a(n) non-separations for n = 12, 36, 60, 72, 180, 420:
%e A336107 (11) (112) (1122) (1123) (11122) (11223) (11234)
%e A336107 (211) (1221) (1132) (11212) (11232) (11243)
%e A336107 (2112) (2113) (11221) (11322) (11324)
%e A336107 (2211) (2311) (12112) (12213) (11342)
%e A336107 (3112) (12211) (12231) (11423)
%e A336107 (3211) (21112) (13122) (11432)
%e A336107 (21121) (13221) (21134)
%e A336107 (21211) (21123) (21143)
%e A336107 (22111) (21132) (23114)
%e A336107 (22113) (23411)
%e A336107 (22131) (24113)
%e A336107 (22311) (24311)
%e A336107 (23112) (31124)
%e A336107 (23211) (31142)
%e A336107 (31122) (32114)
%e A336107 (31221) (32411)
%e A336107 (32112) (34112)
%e A336107 (32211) (34211)
%e A336107 (41123)
%e A336107 (41132)
%e A336107 (42113)
%e A336107 (42311)
%e A336107 (43112)
%e A336107 (43211)
%t A336107 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A336107 Table[Length[Select[Permutations[primeMS[n]],MatchQ[#,{___,x_,x_,___}]&]],{n,100}]
%Y A336107 A005117 lists positions of zeros, with complement A013929.
%Y A336107 A008480 counts permutations of prime indices, ranked by A333221.
%Y A336107 A003242 and A335452 count separations, ranked by A333489.
%Y A336107 A325535 counts inseparable partitions, ranked by A335448.
%Y A336107 A325534 counts separable partitions, ranked by A335433.
%Y A336107 Cf. A056239, A112798, A261962, A335451, A335452, A335460, A335489.
%K A336107 nonn
%O A336107 1,12
%A A336107 _Gus Wiseman_, Sep 03 2020