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 A325363 Heinz numbers of integer partitions into nonzero triangular numbers A000217. 1
 1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 29, 32, 40, 47, 50, 52, 58, 64, 65, 73, 80, 94, 100, 104, 107, 116, 125, 128, 130, 145, 146, 151, 160, 169, 188, 197, 200, 208, 214, 232, 235, 250, 256, 257, 260, 290, 292, 302, 317, 320, 325, 338, 365, 376, 377, 394, 397 (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 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}     4: {1,1}     5: {3}     8: {1,1,1}    10: {1,3}    13: {6}    16: {1,1,1,1}    20: {1,1,3}    25: {3,3}    26: {1,6}    29: {10}    32: {1,1,1,1,1}    40: {1,1,1,3}    47: {15}    50: {1,3,3}    52: {1,1,6}    58: {1,10}    64: {1,1,1,1,1,1}    65: {3,6} MATHEMATICA nn=1000; primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; trgs=Table[n*(n+1)/2, {n, Sqrt[2*PrimePi[nn]]}]; Select[Range[nn], SubsetQ[trgs, primeMS[#]]&] CROSSREFS Cf. A000217, A007294, A056239, A112798, A240026, A325327, A325360, A325362, A325367, A325390, A325394, A325400. Sequence in context: A144876 A239517 A231056 * A000549 A191985 A126026 Adjacent sequences:  A325360 A325361 A325362 * A325364 A325365 A325366 KEYWORD nonn AUTHOR Gus Wiseman, May 02 2019 STATUS approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)