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 A325394 Heinz numbers of integer partitions whose augmented differences are weakly increasing. 15
 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 64, 67, 71, 73, 75, 77, 79, 81, 83, 89, 91, 97, 101, 103, 105, 107, 109, 113, 119, 121, 125, 127, 128, 131, 137, 139, 143, 149, 151, 157, 163, 167 (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 augmented differences aug(y) of an integer partition y of length k are given by aug(y)_i = y_i - y_{i + 1} + 1 if i < k and aug(y)_k = y_k. For example, aug(6,5,5,3,3,3) = (2,1,3,1,1,3). The enumeration of these partitions by sum is given by A325356. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     4: {1,1}     5: {3}     7: {4}     8: {1,1,1}     9: {2,2}    11: {5}    13: {6}    15: {2,3}    16: {1,1,1,1}    17: {7}    19: {8}    23: {9}    25: {3,3}    27: {2,2,2}    29: {10}    31: {11}    32: {1,1,1,1,1} MATHEMATICA primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]]; aug[y_]:=Table[If[i

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Last modified January 19 18:13 EST 2020. Contains 331051 sequences. (Running on oeis4.)