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 A316904 Heinz numbers of aperiodic integer partitions into relatively prime parts whose reciprocal sum is an integer. 17
 2, 18, 72, 162, 195, 250, 288, 294, 390, 500, 588, 648, 780, 1125, 1152, 1176, 1458, 1560, 1755, 2000, 2250, 2352, 2592, 2646, 3120, 3185, 3510, 4000, 4500, 4608, 4704, 4802, 5292, 6240, 6370, 6475, 7020, 8450, 9000, 9408, 10125, 10368, 10527, 10584, 12480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). A partition is aperiodic if its multiplicities are relatively prime. LINKS Table of n, a(n) for n=1..45. Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums EXAMPLE The sequence of partitions whose Heinz numbers belong to this sequence begins: (1), (221), (22111), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111). MATHEMATICA Select[Range[2, 20000], And[GCD@@FactorInteger[#][[All, 2]]==1, GCD@@PrimePi/@FactorInteger[#][[All, 1]]==1, IntegerQ[Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&] CROSSREFS Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904. Sequence in context: A258929 A034959 A316902 * A196812 A163102 A073976 Adjacent sequences: A316901 A316902 A316903 * A316905 A316906 A316907 KEYWORD nonn AUTHOR Gus Wiseman, Jul 16 2018 STATUS approved

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Last modified June 7 21:29 EDT 2023. Contains 363157 sequences. (Running on oeis4.)