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%I #5 Feb 24 2020 21:56:39
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,
%T 0,3,0,0,0,0,0,2,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,6,0,0,0,0,0,2,0,0,
%U 0,2,0,6,0,0,1,0,0,2,0,0,0,0,0,6,0,0,0
%N Number of non-unimodal permutations of the multiset of prime indices of n.
%C 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 A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
%H MathWorld, <a href="http://mathworld.wolfram.com/UnimodalSequence.html">Unimodal Sequence</a>
%F a(n) + A332288(n) = A008480(n).
%F a(A181821(n)) = A332672(n).
%e The a(n) permutations for n = 18, 30, 36, 42, 50, 54, 60, 66, 70, 72:
%e 212 213 1212 214 313 2122 1213 215 314 11212
%e 312 2112 412 2212 1312 512 413 12112
%e 2121 2113 12121
%e 2131 21112
%e 3112 21121
%e 3121 21211
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t unimodQ[q_]:=Or[Length[q]<=1,If[q[[1]]<=q[[2]],unimodQ[Rest[q]],OrderedQ[Reverse[q]]]];
%t Table[Length[Select[Permutations[primeMS[n]],!unimodQ[#]&]],{n,100}]
%Y Dominated by A008480.
%Y The complement is counted by A332288.
%Y A more interesting version is A332672.
%Y Unimodal compositions are A001523.
%Y Non-unimodal permutations are A059204.
%Y Non-unimodal compositions are A115981.
%Y Non-unimodal normal sequences are A328509.
%Y Heinz numbers of partitions with non-unimodal run-lengths are A332282.
%Y Compositions whose negation is not unimodal are A332669.
%Y Cf. A007052, A056239, A112798, A124010, A332281, A332284, A332287, A332294, A332639, A332642.
%K nonn
%O 1,30
%A _Gus Wiseman_, Feb 22 2020
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