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A063958
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Sum of the non-unitary prime factors of n: sum of those prime factors for which the exponent exceeds 1.
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5
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0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 5, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 2, 3, 0, 0, 2, 7, 5, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 0, 3, 2, 0, 0, 0, 2, 0, 0, 0, 5, 0, 0, 5, 2, 0, 0, 0, 2, 3, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 2, 0, 0, 0, 2, 0, 7, 3, 7, 0, 0, 0, 2, 0
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OFFSET
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1,4
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k) * x^(prime(k)^2) / (1 - x^(prime(k)^2)). - Ilya Gutkovskiy, Apr 06 2020
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MAPLE
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a:= proc(n) option remember; add(`if`(i[2]>1, i[1], 0), i=ifactors(n)[2]) end:
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MATHEMATICA
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Array[Total@ Select[FactorInteger@ #, Last@ # > 1 &][[All, 1]] &, 105] (* Michael De Vlieger, Dec 06 2018 *)
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PROG
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(PARI) { for (n=1, 1000, f=factor(n)~; a=0; for (i=1, length(f), if (f[2, i]>1, a+=f[1, i])); write("b063958.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 04 2009
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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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