A318587 Heinz numbers of integer partitions whose sum of reciprocals squared is 1.

2, 81, 8775, 64827, 950625, 1953125, 7022925, 9055935, 21781575, 36020025, 50124555, 51883209, 57909033, 102984375, 118978125, 760816875, 816747435, 981059625, 1206902781, 1265058675, 1387132263, 2359670625, 3902169375, 4868424351, 5222768733, 5430160125

Offset: 1

Author

Gus Wiseman, Aug 29 2018

Keywords

• nonn

Comments

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

Examples

			The sequence of integer partitions with Heinz numbers in this sequence begins: (1), (2222), (633222), (4444222), (66333322).
		

Crossrefs

Cf. A001222, A051908, A056239, A112798, A289506, A289507, A316855, A316856, A316857.

Cf. A318584, A318585, A318586, A318588, A318589.

Programs

Mathematica

Select[Range[100000],Total[If[#==1,{},Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]^2]]]==1&]

Extensions

a(6)-a(26) from Alois P. Heinz, Aug 30 2018