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 A325362 Heinz numbers of integer partitions whose differences (with the last part taken to be 0) are weakly increasing. 12
 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 57, 58, 59, 61, 62, 65, 66, 67, 69, 71, 73, 74, 78, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 101, 102, 103, 106, 107, 109, 110, 111, 113 (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 (x, y, z) are (y - x, z - y). We adhere to this standard for integer partitions also even though they are always weakly decreasing. 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 A007294. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     5: {3}     6: {1,2}     7: {4}    10: {1,3}    11: {5}    13: {6}    14: {1,4}    17: {7}    19: {8}    21: {2,4}    22: {1,5}    23: {9}    26: {1,6}    29: {10}    30: {1,2,3}    31: {11}    33: {2,5} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], OrderedQ[Differences[Append[primeptn[#], 0]]]&] CROSSREFS Cf. A007294, A056239, A112798, A240026, A320348, A325327, A325360, A325364, A325367, A325390, A325394, A325400. Sequence in context: A087006 A235991 A327906 * A325396 A326533 A144147 Adjacent sequences:  A325359 A325360 A325361 * A325363 A325364 A325365 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

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Last modified December 5 20:45 EST 2019. Contains 329779 sequences. (Running on oeis4.)