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

1,1

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).

Links

Table of n, a(n) for n=1..37.

Example

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).

Mathematica

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

Crossrefs

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

Sequence in context: A237999 A194017 A135543 * A088862 A062457 A307539

Adjacent sequences: A316852 A316853 A316854 * A316856 A316857 A316858

Keyword

nonn

Author

Gus Wiseman, Jul 14 2018

Status

approved