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

1,1

Comments

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..26.

Example

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

Mathematica

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

Crossrefs

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

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

Sequence in context: A187858 A352742 A072408 * A302722 A123177 A209585

Adjacent sequences: A318584 A318585 A318586 * A318588 A318589 A318590

Keyword

nonn

Author

Gus Wiseman, Aug 29 2018

Extensions

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

Status

approved