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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
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.
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[#]}]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
STATUS
approved