

A332643


Neither the unsorted prime signature of a(n) nor the negated unsorted prime signature of a(n) is unimodal.


11



2100, 3300, 3900, 4200, 4410, 5100, 5700, 6468, 6600, 6900, 7644, 7800, 8400, 8700, 9300, 9996, 10200, 10500, 10780, 10890, 11100, 11172, 11400, 12300, 12740, 12900, 12936, 13200, 13230, 13524, 13800, 14100, 15210, 15246, 15288, 15600, 15900, 16500, 16660
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OFFSET

1,1


COMMENTS

A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization.


LINKS



FORMULA



EXAMPLE

The sequence of terms together with their prime indices begins:
2100: {1,1,2,3,3,4}
3300: {1,1,2,3,3,5}
3900: {1,1,2,3,3,6}
4200: {1,1,1,2,3,3,4}
4410: {1,2,2,3,4,4}
5100: {1,1,2,3,3,7}
5700: {1,1,2,3,3,8}
6468: {1,1,2,4,4,5}
6600: {1,1,1,2,3,3,5}
6900: {1,1,2,3,3,9}
7644: {1,1,2,4,4,6}
7800: {1,1,1,2,3,3,6}
8400: {1,1,1,1,2,3,3,4}
8700: {1,1,2,3,3,10}
9300: {1,1,2,3,3,11}
9996: {1,1,2,4,4,7}
10200: {1,1,1,2,3,3,7}
10500: {1,1,2,3,3,3,4}
10780: {1,1,3,4,4,5}
10890: {1,2,2,3,5,5}


MATHEMATICA

unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]]
Select[Range[10000], !unimodQ[Last/@FactorInteger[#]]&&!unimodQ[Last/@FactorInteger[#]]&]


CROSSREFS

Not requiring nonunimodal negation gives A332282.
These are the Heinz numbers of the partitions counted by A332640.
Not requiring nonunimodality gives A332642.
The case of compositions is A332870.
Nonunimodal permutations are A059204.
Nonunimodal compositions are A115981.
Unsorted prime signature is A124010.
Nonunimodal normal sequences are A328509.
Partitions whose 0appended first differences are unimodal are A332283, with Heinz numbers the complement of A332287.
Compositions whose negation is unimodal are A332578.
Compositions whose negation is not unimodal are A332669.
Partitions whose 0appended first differences are not unimodal are A332744, with Heinz numbers A332832.
Numbers whose signature is neither increasing nor decreasing are A332831.
Cf. A007052, A056239, A072704, A112798, A242031, A242414, A332280, A332281, A332288, A332294, A332639, A332728, A332742.


KEYWORD

nonn


AUTHOR



STATUS

approved



