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A244963
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a(n) = sigma(n) - n * Product_{p|n, p prime} (1 + 1/p).
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5
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0, 0, 0, 1, 0, 0, 0, 3, 1, 0, 0, 4, 0, 0, 0, 7, 0, 3, 0, 6, 0, 0, 0, 12, 1, 0, 4, 8, 0, 0, 0, 15, 0, 0, 0, 19, 0, 0, 0, 18, 0, 0, 0, 12, 6, 0, 0, 28, 1, 3, 0, 14, 0, 12, 0, 24, 0, 0, 0, 24, 0, 0, 8, 31, 0, 0, 0, 18, 0, 0, 0, 51, 0, 0, 4, 20, 0, 0, 0, 42, 13
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OFFSET
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1,8
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COMMENTS
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a(n) = 0 if and only if n is a squarefree number (A005117), otherwise a(n) > 0.
If n is semiprime, then a(n) = 1+floor(sqrt(n))-ceiling(sqrt(n)). - Wesley Ivan Hurt, Dec 25 2016
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c*n^2 + O(n*log(n)), where c = Pi^2/12 - 15/(2*Pi^2) = 0.062558... - Amiram Eldar, Mar 02 2021
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MAPLE
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A244963:= n -> numtheory:-sigma(n) - n*mul(1+1/t[1], t=ifactors(n)[2]):
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MATHEMATICA
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nn = 200; Table[Sum[d, {d, Divisors[n]}], {n, 1, nn}] -
Table[Sum[n/d Abs[MoebiusMu[d]], {d, Divisors[n]}], {n, 1, nn}] (* Geoffrey Critzer, Mar 18 2015 *)
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PROG
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(PARI)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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