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 A325457 Heinz numbers of integer partitions with strictly decreasing differences. 10
 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 70, 71, 73, 74, 75, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 98 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). The differences of a sequence are defined as if the sequence were increasing, so for example the differences of (6,3,1) are (-3,-2). The enumeration of these partitions by sum is given by A320470. LINKS EXAMPLE The sequence of terms together with their prime indices begins:    1: {}    2: {1}    3: {2}    4: {1,1}    5: {3}    6: {1,2}    7: {4}    9: {2,2}   10: {1,3}   11: {5}   12: {1,1,2}   13: {6}   14: {1,4}   15: {2,3}   17: {7}   19: {8}   20: {1,1,3}   21: {2,4}   22: {1,5}   23: {9} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], Greater@@Differences[primeptn[#]]&] CROSSREFS Cf. A056239, A112798, A320470, A320510, A325328, A325352, A325360, A325361, A325368, A325399, A325456, A325461, A320470, A325396. Sequence in context: A340682 A166155 A342525 * A063538 A167207 A037143 Adjacent sequences:  A325454 A325455 A325456 * A325458 A325459 A325460 KEYWORD nonn AUTHOR Gus Wiseman, May 03 2019 STATUS approved

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Last modified July 24 00:28 EDT 2021. Contains 346265 sequences. (Running on oeis4.)