A316855 Heinz numbers of integer partitions whose reciprocal sum is 1.

2, 9, 125, 147, 195, 2401, 3185, 4225, 6475, 6591, 7581, 10101, 10527, 16401, 20445, 20535, 21045, 25365, 46155, 107653, 123823, 142805, 161051, 164255, 164983, 171941, 218855, 228085, 267883, 304175, 312785, 333925, 333935, 335405, 343735, 355355, 390963

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).

Examples

			Sequence of all integer partitions whose reciprocal sum is 1 begins: (1), (2,2), (3,3,3), (4,4,2), (6,3,2), (4,4,4,4), (6,4,4,3), (6,6,3,3), (12,4,3,3), (6,6,6,2), (8,8,4,2).
		

Crossrefs

Cf. A000041, A051908, A056239, A058360, A072411, A296150, A316854, A316856, A316857.

Programs

Mathematica

Select[Range[2,10000],Sum[m[[2]]/PrimePi[m[[1]]],{m,FactorInteger[#]}]==1&]