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 A325366 Heinz numbers of integer partitions whose augmented differences are distinct. 15
 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 17, 19, 21, 22, 23, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 99, 101, 102, 103 (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 A325349. LINKS EXAMPLE The sequence of terms together with their prime indices begins:     1: {}     2: {1}     3: {2}     5: {3}     6: {1,2}     7: {4}     9: {2,2}    10: {1,3}    11: {5}    13: {6}    14: {1,4}    17: {7}    19: {8}    21: {2,4}    22: {1,5}    23: {9}    25: {3,3}    26: {1,6}    29: {10}    31: {11} 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 April 21 10:07 EDT 2021. Contains 343148 sequences. (Running on oeis4.)