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A146076
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Sum of even divisors of n.
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26
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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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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
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a(2k-1) = 0, a(2k) = 2*sigma(k) for positive k.
Dirichlet g.f.: zeta(s - 1)*zeta(s)*2^(1 - s). - Geoffrey Critzer, Mar 29 2015
a(n) = A000203(n) - A000593(n). - Omar E. Pol, Apr 05 2016
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
a(n) = A000203(n)*(1 - (1/A038712(n))). - Omar E. Pol, Aug 01 2018
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MAPLE
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A146076 := proc(n)
if type(n, 'even') then
2*numtheory[sigma](n/2) ;
else
0;
end if;
end proc: # R. J. Mathar, Dec 07 2017
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MATHEMATICA
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f[n_] := Plus @@ Select[Divisors[n], EvenQ]; Array[f, 150] (* Vincenzo Librandi, May 17 2013 *)
a[n_] := DivisorSum[n, Boole[EvenQ[#]]*#&]; Array[a, 100] (* Jean-François Alcover, Dec 01 2015 *)
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 *)
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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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Cf. A000203, A000593, A006128, A038712, A074400, A183063.
Sequence in context: A290971 A178636 A046520 * A157195 A019781 A335959
Adjacent sequences: A146073 A146074 A146075 * A146077 A146078 A146079
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Apr 09 2009
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EXTENSIONS
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Corrected by Jaroslav Krizek, May 07 2011
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STATUS
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approved
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