A326845 Sum times maximum of the integer partition with Heinz number n.

0, 1, 4, 2, 9, 6, 16, 3, 8, 12, 25, 8, 36, 20, 15, 4, 49, 10, 64, 15, 24, 30, 81, 10, 18, 42, 12, 24, 100, 18, 121, 5, 35, 56, 28, 12, 144, 72, 48, 18, 169, 28, 196, 35, 21, 90, 225, 12, 32, 21, 63, 48, 256, 14, 40, 28, 80, 110, 289, 21, 324, 132, 32, 6, 54, 40

Offset: 1

Author

Gus Wiseman, Jul 26 2019

Keywords

• nonn

Comments

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

Crossrefs

Cf. A056239, A061395, A106529, A112798, A316413, A326836, A326844, A326846.

Programs

Mathematica

Table[If[n==1,0,With[{y=Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]},Total[y]*Max[y]]],{n,100}]

Formula

a(n) = A056239(n) * A061395(n).