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A345354
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a(n) = Sum_{p|n, p prime} omega(n/p).
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3
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0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 1, 0, 3, 0, 3, 2, 2, 0, 3, 1, 2, 1, 3, 0, 6, 0, 1, 2, 2, 2, 4, 0, 2, 2, 3, 0, 6, 0, 3, 3, 2, 0, 3, 1, 3, 2, 3, 0, 3, 2, 3, 2, 2, 0, 7, 0, 2, 3, 1, 2, 6, 0, 3, 2, 6, 0, 4, 0, 2, 3, 3, 2, 6, 0, 3, 1, 2, 0, 7, 2, 2, 2, 3, 0, 7, 2, 3
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OFFSET
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1,6
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LINKS
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FORMULA
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a(p) = 0 for p prime.
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EXAMPLE
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a(30) = Sum_{p|30} omega(30/p) = omega(15) + omega(10) + omega(6) = 2 + 2 + 2 = 6.
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MATHEMATICA
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Table[Sum[PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
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PROG
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(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, omega(n/f[k, 1])); \\ Michel Marcus, Jun 16 2021
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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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