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

Offset: 0

Author

Gus Wiseman, May 07 2019

Keywords

• nonn

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.

Crossrefs

Cf. A001222, A003963, A015716, A015723, A022629, A056239, A066189, A112798, A147655, A246867, A325504, A325506.

Programs

Mathematica

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

Formula

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