A316895 - OEIS

A316895

Number of aperiodic integer partitions of n whose reciprocal sum is an integer.

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

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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.

LINKS

Table of n, a(n) for n=1..60.

Gus Wiseman, Sequences counting and ranking integer partitions by their reciprocal sums

EXAMPLE

The a(11) = 5 partitions are (632), (4421), (33311), (2222111), (221111111).

MATHEMATICA