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 A325460 Heinz numbers of integer partitions with strictly increasing differences (with the last part taken to be 0). 9
 1, 2, 3, 5, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 33, 34, 37, 38, 39, 41, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 122, 123, 127, 129, 130, 131 (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) (with the last part taken to be 0) are (-3,-2,-1). The enumeration of these partitions by sum is given by A179269. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     5: {3}     7: {4}    10: {1,3}    11: {5}    13: {6}    14: {1,4}    17: {7}    19: {8}    22: {1,5}    23: {9}    26: {1,6}    29: {10}    31: {11}    33: {2,5}    34: {1,7}    37: {12}    38: {1,8} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], Less@@Differences[Append[primeptn[#], 0]]&] CROSSREFS A subsequence of A005117. Cf. A007294, A056239, A112798, A179269, A325327, A325362, A325364, A325367, A325388, A325390, A325395, A325398, A325456, A325461. Sequence in context: A118241 A325160 A258613 * A002269 A327445 A325119 Adjacent sequences:  A325457 A325458 A325459 * A325461 A325462 A325463 KEYWORD nonn AUTHOR Gus Wiseman, May 03 2019 STATUS approved

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Last modified January 28 10:02 EST 2020. Contains 331319 sequences. (Running on oeis4.)