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A113418 Expansion of (eta(q^2)^7*eta(q^4)/(eta(q)*eta(q^8))^2-1)/2 in powers of q. 1
1, -1, -2, -1, -4, 2, 8, -1, 7, 4, -10, 2, -12, -8, 8, -1, 18, -7, -18, 4, -16, 10, 24, 2, 21, 12, -20, -8, -28, -8, 32, -1, 20, -18, -32, -7, -36, 18, 24, 4, 42, 16, -42, 10, -28, -24, 48, 2, 57, -21, -36, 12, -52, 20, 40, -8, 36, 28, -58, -8, -60, -32, 56, -1, 48, -20, -66, -18, -48, 32, 72, -7, 74, 36, -42, 18, -80, -24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..78.

FORMULA

a(n) is multiplicative and a(2^e) = -1 if e>0, a(p^e) = (p^(e+1)-1)/(p-1) if p == 1, 7 (mod 8), a(p^e) = ((-p)^(e+1)-1)/(-p-1) if p == 3, 5 (mod 8).

G.f.: Sum_{k>0} (2k-1)*(-1)^[k/2]*x^(2k-1)/(1+x^(2k-1)).

PROG

(PARI) a(n)=if(n<1, 0, -sumdiv(n, d, d*(d%2)*(-1)^(n/d+(d+1)\4)))

(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, -1, p*=kronecker(2, p); (p^(e+1)-1)/(p-1)))))}

CROSSREFS

Apart from signs, same as A117000.

A113416(n)=2*a(n) if n>0.

Sequence in context: A079966 A101707 A304587 * A117000 A082392 A233327

Adjacent sequences:  A113415 A113416 A113417 * A113419 A113420 A113421

KEYWORD

sign,mult

AUTHOR

Michael Somos, Oct 29 2005

STATUS

approved

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Last modified October 16 13:21 EDT 2019. Contains 328083 sequences. (Running on oeis4.)