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A325515 Sum of sums of omegas of the parts over all strict integer partitions of n. 4
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 (list; graph; refs; listen; history; text; internal format)
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}]

CROSSREFS

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

Sequence in context: A194221 A054925 A194248 * A126097 A024611 A131073

Adjacent sequences:  A325512 A325513 A325514 * A325516 A325517 A325518

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 07 2019

STATUS

approved

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Last modified November 14 12:33 EST 2019. Contains 329114 sequences. (Running on oeis4.)