OFFSET
1,1
COMMENTS
The unsorted prime signature of a positive integer (row n of A124010) is the sequence of exponents it is prime factorization.
A sequence of positive integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
Also Heinz numbers of integer partitions with non-unimodal run-lengths. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
MathWorld, Unimodal Sequence
EXAMPLE
The sequence of terms together with their prime indices begins:
300: {1,1,2,3,3}
588: {1,1,2,4,4}
600: {1,1,1,2,3,3}
980: {1,1,3,4,4}
1176: {1,1,1,2,4,4}
1200: {1,1,1,1,2,3,3}
1452: {1,1,2,5,5}
1500: {1,1,2,3,3,3}
1960: {1,1,1,3,4,4}
2028: {1,1,2,6,6}
2100: {1,1,2,3,3,4}
2205: {2,2,3,4,4}
2352: {1,1,1,1,2,4,4}
2400: {1,1,1,1,1,2,3,3}
2420: {1,1,3,5,5}
2904: {1,1,1,2,5,5}
2940: {1,1,2,3,4,4}
3000: {1,1,1,2,3,3,3}
3300: {1,1,2,3,3,5}
3380: {1,1,3,6,6}
MATHEMATICA
unimodQ[q_]:=Or[Length[q]==1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Select[Range[1000], !unimodQ[Last/@FactorInteger[#]]&]
CROSSREFS
The opposite version is A332642.
These are the Heinz numbers of the partitions counted by A332281.
Non-unimodal permutations are A059204.
Non-unimodal compositions are A115981.
Non-unimodal normal sequences are A328509.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 19 2020
STATUS
approved