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A344931
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Sum of the distinct even-indexed prime divisors, p_{2k}, of n.
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3
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0, 0, 3, 0, 0, 3, 7, 0, 3, 0, 0, 3, 13, 7, 3, 0, 0, 3, 19, 0, 10, 0, 0, 3, 0, 13, 3, 7, 29, 3, 0, 0, 3, 0, 7, 3, 37, 19, 16, 0, 0, 10, 43, 0, 3, 0, 0, 3, 7, 0, 3, 13, 53, 3, 0, 7, 22, 29, 0, 3, 61, 0, 10, 0, 13, 3, 0, 0, 3, 7, 71, 3, 0, 37, 3, 19, 7, 16, 79, 0, 3, 0, 0, 10, 0, 43, 32
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = Sum_{p|n} p * ((pi(p)+1) mod 2 ).
G.f.: Sum_{k>=1} prime(2*k) * x^prime(2*k) / (1 - x^prime(2*k)). - Ilya Gutkovskiy, Oct 24 2023
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EXAMPLE
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a(12) = Sum_{p|12} p * ((pi(p)+1) mod 2 ) = 2*0 + 3*1 = 3.
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MATHEMATICA
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Table[Sum[k*Mod[PrimePi[k] + 1, 2] (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~, if (!(primepi(f[k, 1]) % 2), f[k, 1])); \\ Michel Marcus, Jun 12 2021
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CROSSREFS
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Cf. A344908 (sum of distinct odd-indexed prime divisors).
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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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