login
A316903
Heinz numbers of aperiodic integer partitions whose reciprocal sum is the reciprocal of an integer.
0
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
1,1
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).
A partition is aperiodic if its multiplicities are relatively prime.
MATHEMATICA
Select[Range[2, 1000], And[GCD@@FactorInteger[#][[All, 2]]==1, IntegerQ[1/Sum[m[[2]]/PrimePi[m[[1]]], {m, FactorInteger[#]}]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2018
STATUS
approved