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

1,5

Comments

The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

Links

Table of n, a(n) for n=1..60.

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A098527 A035635 A114869 * A352828 A029100 A356758

Adjacent sequences: A316896 A316897 A316898 * A316900 A316901 A316902

Keyword

nonn

Author

Gus Wiseman, Jul 16 2018

Extensions

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

Status

approved