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A332282
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Numbers whose unsorted prime signature is not unimodal.
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37
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300, 588, 600, 980, 1176, 1200, 1452, 1500, 1960, 2028, 2100, 2205, 2352, 2400, 2420, 2904, 2940, 3000, 3300, 3380, 3388, 3468, 3900, 3920, 4056, 4116, 4200, 4332, 4410, 4704, 4732, 4800, 4840, 5100, 5445, 5700, 5780, 5808, 5880, 6000, 6348, 6468, 6600, 6615
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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}
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MATHEMATICA
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unimodQ[q_]:=Or[Length[q]==1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]];
Select[Range[1000], !unimodQ[Last/@FactorInteger[#]]&]
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CROSSREFS
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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.
Cf. A001523, A007052, A056239, A112798, A124010, A227038, A332280, A332284, A332286, A332639, A332643, A332671.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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