A316894 Number of aperiodic integer partitions of n whose reciprocal sum is the reciprocal of an integer.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 4, 1, 5, 1, 2, 3, 2, 4, 5, 5, 5, 4, 3, 5, 4, 8, 6, 9, 7, 5, 6, 10, 6, 12, 8, 7, 7, 6, 6, 12, 12, 8, 18, 13, 16, 19, 17, 18, 21, 26, 26, 28, 29, 21, 29, 29, 27, 38, 32, 26, 37, 32, 38, 39, 49, 36, 61, 46, 55

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..78.

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

Mathematica

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

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316857, A316888-A316904.

Sequence in context: A176166 A167911 A037804 * A362933 A081503 A351206

Adjacent sequences: A316891 A316892 A316893 * A316895 A316896 A316897

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

a(51)-a(78) from Giovanni Resta, Jul 16 2018

Status

approved