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 A325405 Heinz numbers of integer partitions y such that the k-th differences of y are distinct for all k >= 0 and are disjoint from the i-th differences for i != k. 17
 1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 17, 19, 22, 23, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A325388 in lacking 130. 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) are (-3,-2). The zeroth differences of a sequence are the sequence itself, while the k-th differences for k > 0 are the differences of the (k-1)-th differences. The enumeration of these partitions by sum is given by A325404. LINKS Table of n, a(n) for n=1..64. Gus Wiseman, Sequences counting and ranking integer partitions by the differences of their successive parts. EXAMPLE The sequence of terms together with their prime indices begins: 1: {} 2: {1} 3: {2} 5: {3} 7: {4} 10: {1,3} 11: {5} 13: {6} 14: {1,4} 15: {2,3} 17: {7} 19: {8} 22: {1,5} 23: {9} 26: {1,6} 29: {10} 31: {11} 33: {2,5} 34: {1,7} 35: {3,4} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], UnsameQ@@Join@@Table[Differences[primeMS[#], k], {k, 0, PrimeOmega[#]}]&] CROSSREFS A subsequence of A005117. Cf. A056239, A112798, A279945, A325325, A325366, A325367, A325368, A325397, A325398, A325399, A325400, A325404, A325406, A325467. Sequence in context: A090421 A109608 A325388 * A118241 A356237 A325160 Adjacent sequences: A325402 A325403 A325404 * A325406 A325407 A325408 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

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Last modified June 6 06:26 EDT 2023. Contains 363139 sequences. (Running on oeis4.)