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A332671
Number of non-unimodal permutations of the multiset of prime indices of n.
11
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, 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, 0, 2, 0, 6, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0
OFFSET
1,30
COMMENTS
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.
A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
FORMULA
a(n) + A332288(n) = A008480(n).
a(A181821(n)) = A332672(n).
EXAMPLE
The a(n) permutations for n = 18, 30, 36, 42, 50, 54, 60, 66, 70, 72:
212 213 1212 214 313 2122 1213 215 314 11212
312 2112 412 2212 1312 512 413 12112
2121 2113 12121
2131 21112
3112 21121
3121 21211
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Table[Length[Select[Permutations[primeMS[n]], !unimodQ[#]&]], {n, 100}]
CROSSREFS
Dominated by A008480.
The complement is counted by A332288.
A more interesting version is A332672.
Unimodal compositions are A001523.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
Heinz numbers of partitions with non-unimodal run-lengths are A332282.
Compositions whose negation is not unimodal are A332669.
Sequence in context: A351254 A356303 A238429 * A074039 A047764 A022883
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 22 2020
STATUS
approved