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 A325367 Heinz numbers of integer partitions with distinct differences between successive parts (with the last part taken to be zero). 17
 1, 2, 3, 4, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 82, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97 (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 enumeration of these partitions by sum is given by A325324. LINKS EXAMPLE The sequence of terms together with their prime indices begins:    1: {}    2: {1}    3: {2}    4: {1,1}    5: {3}    7: {4}    9: {2,2}   10: {1,3}   11: {5}   13: {6}   14: {1,4}   15: {2,3}   17: {7}   19: {8}   20: {1,1,3}   22: {1,5}   23: {9}   25: {3,3}   26: {1,6}   28: {1,1,4} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[200], UnsameQ@@Differences[Append[primeptn[#], 0]]&] CROSSREFS Positions of squarefree numbers in A325390. Cf. A056239, A112798, A130091, A320348, A325324, A325327, A325362, A325364, A325366, A325368, A325388, A325405, A325407, A325460, A325461. Sequence in context: A047363 A191917 A228894 * A160718 A122090 A066050 Adjacent sequences:  A325364 A325365 A325366 * A325368 A325369 A325370 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

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Last modified December 9 09:21 EST 2019. Contains 329877 sequences. (Running on oeis4.)