OFFSET
1,2
COMMENTS
LINKS
W. R. Parry, A negative result on the representation of modular forms by theta series, J. Reine Angew. Math., 310 (1979), 151-170.
FORMULA
a(n) is multiplicative with a(p^e) = (p^(e+1) - 1) / (p - 1) * Kronecker(13, p)^e.
G.f. is a period 1 Fourier series which satisfies f(-1 / (169 t)) = -169 (t/i)^2 f(t) where q = exp(2 Pi i t).
EXAMPLE
q - 3*q^2 + 4*q^3 + 7*q^4 - 6*q^5 - 12*q^6 - 8*q^7 - 15*q^8 + 13*q^9 + ...
MATHEMATICA
Table[If[n==0, 0, DivisorSigma[1, n] JacobiSymbol[13, n]], {n, 100}] (* Indranil Ghosh, Jul 02 2017 *)
PROG
(PARI) {a(n) = if( n==0, 0, sigma(n) * kronecker( 13, n))}
(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]; (p^(e+1) - 1) / (p - 1) * kronecker( 13, p)^e)))}
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Michael Somos, Jun 04 2008
STATUS
approved