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A122071 Sum over divisors d of 2n+1 of Kronecker(-18/d). 2
1, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 3, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

REFERENCES

N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 83, Eq. (32.58).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

FORMULA

Expansion of q^(-1/2)*eta(q^2)^2*eta(q^3)*eta(q^8)*eta(q^12)^3/ (eta(q)*eta(q^4)^2*eta(q^6)*eta(q^24)) in powers of q.

Euler transform of period 24 sequence [1, -1, 0, 1, 1, -1, 1, 0, 0, -1, 1, -2, 1, -1, 0, 0, 1, -1, 1, 1, 0, -1, 1, -2, ...].

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

G.f.: Sum_{k>0} x^k(1-x^(4k-2))(1-x^(6k-3))/(1+x^(12k-6)).

PROG

(PARI) {a(n)=if(n<0, 0, n=2*n+1; sumdiv(n, d, kronecker(-18, d)))}

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^2*eta(x^3+A)*eta(x^8+A)*eta(x^12+A)^3/ eta(x+A)/eta(x^4+A)^2/eta(x^6+A)/eta(x^24+A), n))}

(PARI) {a(n)=local(A, p, e); if(n<0, 0, n=2*n+1; A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 0, if(p==3, 1, if(p%8<4, e+1, (1+(-1)^e)/2))))))}

(PARI) a(n) = sumdiv(2*n+1, d, kronecker(-18, d)); \\ Michel Marcus, Jul 28 2017

CROSSREFS

A035172(2n+1) = a(n).

Sequence in context: A070787 A033985 A216218 * A099766 A194947 A132339

Adjacent sequences:  A122068 A122069 A122070 * A122072 A122073 A122074

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 20 2006

STATUS

approved

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Last modified August 22 07:17 EDT 2019. Contains 326172 sequences. (Running on oeis4.)