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A074400
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Sum of the even divisors of 2n.
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32
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2, 6, 8, 14, 12, 24, 16, 30, 26, 36, 24, 56, 28, 48, 48, 62, 36, 78, 40, 84, 64, 72, 48, 120, 62, 84, 80, 112, 60, 144, 64, 126, 96, 108, 96, 182, 76, 120, 112, 180, 84, 192, 88, 168, 156, 144, 96, 248, 114, 186, 144, 196, 108, 240, 144, 240, 160, 180, 120, 336, 124, 192
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OFFSET
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1,1
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COMMENTS
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Also alternating row sums of A236106. - Omar E. Pol, Jan 23 2014
Could also be called the twice sigma function, see first formula. - Omar E. Pol, Feb 05 2014
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sigma(n)
Index entries for sequences related to sums of divisors
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FORMULA
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a(n) = 2*sigma(n) = 2*A000203(n).
Dirichlet g.f.: 2*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 06 2016
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EXAMPLE
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The even divisors of 12 are 12, 6, 4, 2, which sum to 24, so a(6) = 24.
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MAPLE
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with(numtheory): seq(2*sigma(n), n=1..65);
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MATHEMATICA
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f[n_] := Plus @@ Select[ Divisors[ 2n], EvenQ]; Array[f, 62] (* Robert G. Wilson v, Apr 09 2011 *)
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PROG
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(PARI) a(n) = 2 * sigma(n); \\ Joerg Arndt, Apr 14 2013
(PARI) a(n) = sumdiv(2*n, d, !(d%2) * d); \\ Michel Marcus, Jan 23 2014
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CROSSREFS
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k times sigma(n), k=1..6: A000203, this sequence, A272027, A239050, A274535, A274536.
Cf. A146076, which includes the zeros for odd n.
Sequence in context: A002511 A074383 A107505 * A264598 A165607 A109440
Adjacent sequences: A074397 A074398 A074399 * A074401 A074402 A074403
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KEYWORD
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easy,nonn
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AUTHOR
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Joseph L. Pe, Nov 25 2002
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EXTENSIONS
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More terms from Emeric Deutsch, May 24 2004
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STATUS
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approved
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