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Search: id:A115607
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| A115607 |
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Sum of odd divisors of n times (-1)^(n+1). |
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+0
1
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| 1, -1, 4, -1, 6, -4, 8, -1, 13, -6, 12, -4, 14, -8, 24, -1, 18, -13, 20, -6, 32, -12, 24, -4, 31, -14, 40, -8, 30, -24, 32, -1, 48, -18, 48, -13, 38, -20, 56, -6, 42, -32, 44, -12, 78, -24, 48, -4, 57, -31, 72, -14, 54, -40, 72, -8, 80, -30, 60, -24, 62, -32, 104, -1, 84, -48, 68, -18, 96, -48, 72, -13, 74, -38, 124
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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C. G. J. Jacobi, Gesammelte Werke, vol. 2, 1969, Chelsea, NY, p. 179 eq (6.)
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FORMULA
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Moebius transform is [1, -2, 3, 0, 5, -6, 7, 0, 9, -10, 11, 0, ...].
a(n) is multiplicative with a(2^e) = -1 if e>0, a(p^e) = (p(e+1)-1)/(p-1) if p>2.
G.f.: (theta_2(q)^4 - theta_4(q)^4 +1)/24.
G.f.: Sum_{k>0} -k(-x)^k/(1+(-x)^k) = Sum_{k>0} x^k/(1-(-x)^k)^2.
G.f.: Sum_{k>0} (2k-1)*x^(2k-1)/(1+x^(2k-1)) = Sum_{k>0} x^k/(1-x^k)^2 - 4*x^(4k-2)/(1-x^(4k-2))^2.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (-1)^(n+d)*n/d))
(PARI) a(n)=if(n<1, 0, -(-1)^n*sumdiv(n, d, d%2*d))
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CROSSREFS
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Cf. a(n)=-(-1)^n*A000593(n). A103640(n)=-24*a(n) if n>0.
Adjacent sequences: A115604 A115605 A115606 this_sequence A115608 A115609 A115610
Sequence in context: A117001 A098986 A000593 this_sequence A076717 A120422 A110312
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Jan 26 2006
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