A316891 Number of aperiodic integer partitions of n into relatively prime parts whose reciprocal sum is an integer.

1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 5, 2, 7, 4, 7, 6, 13, 7, 18, 12, 20, 17, 32, 20, 39, 31, 47, 45, 74, 56, 96, 83, 109, 105, 151, 130, 199, 183, 234, 232, 319, 286, 404, 386, 473, 488, 638, 599, 782, 767, 931, 960, 1197, 1165, 1465, 1477, 1747, 1814, 2212, 2196

Offset: 1

Author

Gus Wiseman, Jul 16 2018

Keywords

• nonn

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.

Examples

			The a(17) = 13 partitions:
(6443),
(44441),
(3332222), (6322211),
(44222111),
(222222221), (333221111), (632111111),
(4421111111),
(22222211111), (33311111111),
(2222111111111),
(221111111111111).
		

Links

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

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316856, A316888-A316904.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,GCD@@Length/@Split[#]==1,IntegerQ[Sum[1/m,{m,#}]]]&]],{n,50}]

Extensions

a(51)-a(60) from Alois P. Heinz, Jul 18 2018