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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
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
Sequence in context: A258929 A034959 A316902 * A196812 A163102 A073976
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
STATUS
approved

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)