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A113184
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Difference between sum of odd divisors of n and sum of even divisors of n.
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4
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1, 1, 4, 5, 6, 4, 8, 13, 13, 6, 12, 20, 14, 8, 24, 29, 18, 13, 20, 30, 32, 12, 24, 52, 31, 14, 40, 40, 30, 24, 32, 61, 48, 18, 48, 65, 38, 20, 56, 78, 42, 32, 44, 60, 78, 24, 48, 116, 57, 31, 72, 70, 54, 40, 72, 104, 80, 30, 60, 120, 62, 32, 104, 125, 84, 48, 68, 90, 96, 48, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The generating function equals 1/8 at q = Lambda = 0.1076539192... (A072558) the "One-Ninth" constant. - Michael Somos Jul 21 2006
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| Multiplicative with a(2^e) = 2^(e+1)-3 if e>0, a(p^e) = (p^(e+1)-1)/(p-1) if p>2.
G.f.: Sum_{k>0} -(-x)^k/(1+(-x)^k)^2 = Sum_{k>0} k*x^k/(1-(-x)^k).
Expansion of (1-(2/pi)^2(2E(k)-K(k))K(k))/8 in powers of nome q where E(k) and K(k) are complete elliptic integrals and q=exp(-pi*K(k')/K(k)). - Michael Somos Jul 21 2006
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MATHEMATICA
| f[n_]:=Module[{dn=Divisors[n], odn, edn}, odn=Select[dn, OddQ]; edn=Select[dn, EvenQ]; Abs[Total[odn]-Total[edn]]]
f/@Range[80] (* From Harvey P. Dale, Feb 25 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 0, (-1)^n*sumdiv(n, d, (-1)^d*d))
(PARI) {a(n)=local(A, p, e); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 2^(e+1)-3, (p^(e+1)-1)/(p-1)))))}
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CROSSREFS
| Cf. A002129(n)=-(-1)^n a(n).
Sequence in context: A196999 A090370 A002129 * A136004 A134299 A112780
Adjacent sequences: A113181 A113182 A113183 * A113185 A113186 A113187
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Oct 17 2005
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