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A316895
Number of aperiodic integer partitions of n whose reciprocal sum is an integer.
0
1, 0, 0, 0, 1, 0, 1, 0, 2, 2, 5, 2, 7, 5, 7, 6, 13, 8, 18, 13, 20, 19, 32, 21, 39, 35, 49, 48, 74, 60, 96, 86, 110, 111, 151, 135, 199, 192, 235, 239, 319, 299, 404, 394, 477, 506, 638, 609, 782, 788, 934, 978, 1197, 1193, 1466, 1501, 1752, 1851, 2212, 2227
OFFSET
1,9
COMMENTS
The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
A partition is aperiodic if its multiplicities are relatively prime.
EXAMPLE
The a(11) = 5 partitions are (632), (4421), (33311), (2222111), (221111111).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And[GCD@@Length/@Split[#]==1, IntegerQ[Sum[1/m, {m, #}]]]&]], {n, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
EXTENSIONS
a(51)-a(60) from Alois P. Heinz, Jul 17 2018
STATUS
approved