

A332672


Number of nonunimodal permutations of a multiset whose multiplicities are the prime indices of n.


10



0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 6, 0, 0, 6, 16, 0, 21, 0, 12, 10, 0, 0, 48, 16, 0, 81, 20, 0, 48, 0, 104, 15, 0, 30, 162, 0, 0, 21, 104, 0, 90, 0, 30, 198, 0, 0, 336, 65, 124, 28, 42, 0, 603, 50, 190, 36, 0, 0, 396, 0, 0, 405, 688, 77, 150, 0, 56, 45, 260, 0
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OFFSET

1,8


COMMENTS

This multiset is generally not the same as the multiset of prime indices of n. For example, the prime indices of 12 are {1,1,2}, while a multiset whose multiplicities are {1,1,2} is {1,1,2,3}.
A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.


LINKS

Table of n, a(n) for n=1..71.
MathWorld, Unimodal Sequence


FORMULA

a(n) = A332671(A181821(n)).
a(n) + A332294(n) = A318762(n).


EXAMPLE

The a(n) permutations for n = 8, 9, 12, 15, 16:
213 1212 1213 11212 1324
312 2112 1312 12112 1423
2121 2113 12121 2134
2131 21112 2143
3112 21121 2314
3121 21211 2413
3124
3142
3214
3241
3412
4123
4132
4213
4231
4312


MATHEMATICA

nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]], {#1}]&, If[n==1, {}, Flatten[Cases[FactorInteger[n]//Reverse, {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[nrmptn[n]], !unimodQ[#]&]], {n, 30}]


CROSSREFS

Positions of zeros are one and A001751.
Support is A264828 without one.
Dominated by A318762.
The complement is counted by A332294.
A less interesting version is A332671.
The opposite version is A332742.
Unimodal compositions are A001523.
Nonunimodal permutations are A059204.
Nonunimodal compositions are A115981.
Nonunimodal normal sequences are A328509.
Heinz numbers of partitions with nonunimodal runlengths are A332282.
Compositions whose negation is not unimodal are A332669.
Cf. A007052, A008480, A056239, A112798, A124010, A181819, A181821, A332281, A332287, A332294, A332642, A332741.
Sequence in context: A213714 A242011 A259657 * A184362 A011311 A240658
Adjacent sequences: A332669 A332670 A332671 * A332673 A332674 A332675


KEYWORD

nonn


AUTHOR

Gus Wiseman, Feb 23 2020


STATUS

approved



