A316857 Heinz numbers of integer partitions whose reciprocal sum is the reciprocal of an integer.

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 147, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239

Offset: 1

Author

Gus Wiseman, Jul 14 2018

Keywords

• nonn

Comments

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

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

Crossrefs

Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316855, A316856.

Programs

Mathematica

Select[Range[2,100],IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]&]