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1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 3, 5, 5, 2, 2, 5, 5, 9, 3, 4, 6, 4, 3, 6, 8, 4, 10, 9, 8, 11, 7, 13, 12, 15, 15, 21, 18, 16, 21, 19, 17, 30, 23, 19, 23, 28, 25, 29, 34, 29, 44, 28, 46, 48, 42

nonn,more,changed

a(51)-a(80) from Giovanni Resta, Jul 16 2018

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Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>

The a(37) = 5 partitions are (24,8,3,2), (20,5,4,4,4), (15,10,6,3,3), (14,7,7,7,2), (10,10,10,5,2).

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904.

allocated for Gus WisemanNumber of aperiodic integer partitions of n whose reciprocal sum is 1.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 1, 1, 2, 3, 2, 2, 1, 2, 2, 2, 3, 5, 5, 2, 2, 5, 5, 9, 3, 4, 6, 4, 3, 6, 8

1,22

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.

Table[Length[Select[IntegerPartitions[n], And[GCD@@Length/@Split[#]==1, Sum[1/m, {m, #}]==1]&]], {n, 30}]

Cf. A000837, A051908, A058360, A100953, A316854, A316888-A316904.

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Gus Wiseman, Jul 16 2018

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allocated for Gus Wiseman

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