A316899 Number of integer partitions of n into relatively prime parts whose reciprocal sum is an integer.

1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 6, 6, 8, 8, 10, 10, 14, 14, 19, 20, 25, 29, 33, 34, 41, 47, 54, 61, 75, 81, 97, 103, 121, 132, 155, 164, 200, 221, 252, 274, 320, 348, 405, 442, 501, 554, 639, 688, 784, 854, 968, 1053, 1198, 1298, 1475, 1602, 1797, 1965, 2213, 2399

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.

Examples

			The a(13) = 8 partitions are (63211), (442111), (33322), (3331111), (2222221), (222211111), (22111111111), (1111111111111).
		

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@@#==1,IntegerQ[Sum[1/m,{m,#}]]]&]],{n,30}]

PARI

a(n)={my(s=0); forpart(p=n, if(gcd(p)==1 && frac(sum(i=1, #p, 1/p[i]))==0, s++)); s} \\ Andrew Howroyd, Aug 26 2018

Extensions

a(51)-a(60) from Andrew Howroyd, Aug 26 2018