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A325536
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Sum of sums of omegas of parts over all integer partitions of n.
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1
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0, 0, 1, 2, 6, 9, 19, 28, 51, 75, 119, 170, 261, 362, 525, 723, 1019, 1373, 1890, 2512, 3386, 4452, 5893, 7658, 10017, 12881, 16627, 21210, 27097, 34266, 43392, 54462, 68399, 85285, 106305, 131712, 163132, 200936, 247332, 303066, 370989, 452296, 550875, 668495
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OFFSET
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0,4
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COMMENTS
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Also omega of the product of products of parts over all integer partitions of n.
The omega of n is A001222(n), the number of prime factors of n counted with multiplicity.
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LINKS
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FORMULA
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EXAMPLE
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The integer partitions of 5 are {(5), (4,1), (3,2), (3,1,1), (2,2,1), (2,1,1,1), (1,1,1,1,1)} with products {5,4,6,3,4,2,1} with product 2880 with omega 9, so a(5) = 9.
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MATHEMATICA
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Table[Plus@@PrimeOmega/@Join@@IntegerPartitions[n], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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