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A333842
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G.f.: Sum_{k>=1} k * x^(prime(k)^2) / (1 - x^(prime(k)^2)).
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1
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0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 4, 3, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 3, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 4, 2, 4, 0, 0, 0, 1
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OFFSET
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1,9
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COMMENTS
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Sum of indices of non-unitary prime factors of n (prime factors for which the exponent exceeds 1).
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LINKS
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FORMULA
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EXAMPLE
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a(450) = a(2 * 3^2 * 5^2) = a(prime(1) * prime(2)^2 * prime(3)^2) = 2 + 3 = 5.
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MATHEMATICA
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nmax = 104; CoefficientList[Series[Sum[k x^(Prime[k]^2)/(1 - x^(Prime[k]^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(PARI) A333842(n) = { my(f=factor(n)); sum(k=1, #f~, if(1==f[k, 2], 0, 1)*primepi(f[k, 1])); }; \\ Antti Karttunen, Jun 12 2020
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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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