A316896 Number 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, 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

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(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).
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Extensions

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