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 A325461 Heinz numbers of integer partitions with strictly decreasing differences (with the last part taken to be 0). 7
 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 67, 71, 73, 75, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197 (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 A320510. 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}    11: {5}    13: {6}    15: {2,3}    17: {7}    19: {8}    23: {9}    25: {3,3}    29: {10}    31: {11}    35: {3,4}    37: {12}    41: {13}    43: {14} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; Select[Range[100], Greater@@Differences[Append[primeptn[#], 0]]&] CROSSREFS Cf. A056239, A112798, A320510, A325327, A325362, A325364, A325367, A325388, A325390, A325396, A325399, A325407, A325457, A325460. Sequence in context: A032515 A024926 A051532 * A135785 A262249 A248421 Adjacent sequences:  A325458 A325459 A325460 * A325462 A325463 A325464 KEYWORD nonn AUTHOR Gus Wiseman, May 03 2019 STATUS approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)