A316903 Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 65, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 147, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 195, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257

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.

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

A partition is aperiodic if its multiplicities are relatively prime.

Links

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

Crossrefs

Cf. A000837, A002966, A051908, A058360, A100953, A296150, A316854, A316855, A316856, A316857, A316888-A316904.

Programs

Mathematica

Select[Range[2,1000],And[GCD@@FactorInteger[#][[All,2]]==1,IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]]]&]