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A184389
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a(n) = Sum_{k=1..tau(n)} k, where tau is the number of divisors of n (A000005).
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23
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1, 3, 3, 6, 3, 10, 3, 10, 6, 10, 3, 21, 3, 10, 10, 15, 3, 21, 3, 21, 10, 10, 3, 36, 6, 10, 10, 21, 3, 36, 3, 21, 10, 10, 10, 45, 3, 10, 10, 36, 3, 36, 3, 21, 21, 10, 3, 55, 6, 21, 10, 21, 3, 36, 10, 36, 10, 10, 3, 78, 3, 10, 21, 28, 10, 36, 3, 21, 10, 36, 3, 78
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OFFSET
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1,2
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COMMENTS
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Number of pairs of even divisors of 2n, (d1,d2), such that d1<=d2. - Wesley Ivan Hurt, Aug 24 2020
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LINKS
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FORMULA
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Dirichlet g.f.: zeta(s)^2*(zeta(s)^2 + zeta(2*s))/(2*zeta(2*s)). - Ilya Gutkovskiy, Jun 25 2016
a(n) = Sum_{d1|(2*n), d2|(2*n), d1 and d2 even, d1<=d2} 1. - Wesley Ivan Hurt, Aug 24 2020
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EXAMPLE
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For n = 4; tau(4) = 3; a(4) = 1+2+3 = 6.
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MAPLE
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MATHEMATICA
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((#+1)#)/2&/@DivisorSigma[0, Range[80]] (* Harvey P. Dale, Feb 27 2013 *)
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PROG
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(Haskell)
(PARI) a(n) = my(nd=numdiv(n)); nd*(nd+1)/2; \\ Michel Marcus, Jun 25 2016
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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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