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 A316902 Heinz numbers of aperiodic integer partitions whose reciprocal sum is an integer. 0
 2, 18, 72, 147, 162, 195, 250, 288, 294, 390, 500, 588, 648, 780, 1125, 1152, 1176, 1323, 1458, 1560, 1755, 2000, 2250, 2352, 2592, 2646, 3120, 3185, 3510, 4000, 4500, 4608, 4704, 4802, 5292, 6240, 6370, 6475, 6591, 7020, 7581, 8450, 9000, 9408, 10101, 10125 (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..46. 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), (442), (22221), (632), (3331), (2211111), (4421), (6321), (33311), (44211), (2222111). MATHEMATICA Select[Range[2, 20000], And[GCD@@FactorInteger[#][[All, 2]]==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: A242200 A258929 A034959 * A316904 A196812 A163102 Adjacent sequences: A316899 A316900 A316901 * A316903 A316904 A316905 KEYWORD nonn AUTHOR Gus Wiseman, Jul 16 2018 STATUS approved

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Last modified June 9 18:03 EDT 2023. Contains 363183 sequences. (Running on oeis4.)