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A146076
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Sum of even divisors of n.
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30
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0, 2, 0, 6, 0, 8, 0, 14, 0, 12, 0, 24, 0, 16, 0, 30, 0, 26, 0, 36, 0, 24, 0, 56, 0, 28, 0, 48, 0, 48, 0, 62, 0, 36, 0, 78, 0, 40, 0, 84, 0, 64, 0, 72, 0, 48, 0, 120, 0, 62, 0, 84, 0, 80, 0, 112, 0, 60, 0, 144, 0, 64, 0, 126, 0, 96, 0, 108, 0, 96, 0, 182, 0, 76, 0, 120, 0, 112, 0, 180, 0, 84, 0, 192, 0, 88, 0, 168, 0, 156
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OFFSET
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1,2
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COMMENTS
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The usual OEIS policy is not to include sequences like this where alternate terms are zero; this is an exception. A074400 is the main entry.
a(n) is also the total number of parts in all partitions of n into an even number of equal parts. - Omar E. Pol, Jun 04 2017
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LINKS
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FORMULA
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a(2k-1) = 0, a(2k) = 2*sigma(k) for positive k.
L.g.f.: -log(Product_{ k>0 } (1-x^(2*k))) = Sum_{ n>=0 } (a(n)/n)*x^n. - Benedict W. J. Irwin, Jul 04 2016
Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/24 = 0.411233... (A222171). - Amiram Eldar, Nov 06 2022
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MAPLE
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if type(n, 'even') then
2*numtheory[sigma](n/2) ;
else
0;
end if;
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MATHEMATICA
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f[n_] := Plus @@ Select[Divisors[n], EvenQ]; Array[f, 150] (* Vincenzo Librandi, May 17 2013 *)
Table[CoefficientList[Series[-Log[QPochhammer[x^2, x^2]], {x, 0, 60}], x][[n + 1]] n, {n, 1, 60}] (* Benedict W. J. Irwin, Jul 04 2016 *)
a[n_] := If[OddQ[n], 0, 2*DivisorSigma[1, n/2]]; Array[a, 100] (* Amiram Eldar, Jan 11 2023 *)
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PROG
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(PARI) vector(80, n, if (n%2, 0, sumdiv(n, d, d*(1-(d%2))))) \\ Michel Marcus, Mar 30 2015
(PARI) a(n) = if (n%2, 0, 2*sigma(n/2)); \\ Michel Marcus, Apr 01 2015
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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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EXTENSIONS
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STATUS
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approved
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