A325515 - OEIS

A325515

Sum of sums of omegas of the parts over all strict integer partitions of n.

0, 0, 1, 2, 3, 5, 8, 11, 14, 22, 29, 37, 50, 63, 81, 106, 129, 160, 203, 246, 303, 373, 449, 541, 654, 782, 932, 1116, 1322, 1559, 1848, 2167, 2537, 2978, 3470, 4041, 4706, 5449, 6303, 7291, 8402, 9665, 11117, 12744, 14592, 16708, 19062, 21730, 24757, 28141

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OFFSET

0,4

COMMENTS

Also omega of the product of products of parts over all strict integer partitions of n.

The omega of n is A001222(n), the number of prime factors of n counted with multiplicity.

LINKS

Table of n, a(n) for n=0..49.

FORMULA

a(n) = A001222(A325504(n)).

MATHEMATICA

Table[Sum[Total[PrimeOmega/@s], {s, Select[IntegerPartitions[n], UnsameQ@@#&]}], {n, 0, 30}]