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A082451
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Sum over divisors d of n of Kronecker symbol (-60,d).
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3
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1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 2, 0, 2, 1, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,17
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
Euler transform of period 30 sequence [1,0,0,0,0,-1,1,0,0,-1,1,-1,1,0,0,0,1,-1,1,-1,0,0,1,-1,0,0,0,0,1,-2,...] (if offset 0).
Expansion of eta(q^2)eta(q^3)eta(q^5)eta(q^30)/(eta(q)eta(q^15)) in powers of q.
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| G.f.: x Product_{n>0} (1+x^n)(1-x^(3n))(1-x^(5n))(1+x^(15n)).
a(n) is multiplicative with a(2^e)=a(3^e)=a(5^e)=1, a(p^e) = e+1 if p == 1,2,4,8 (mod 15), a(p^e) = (1+(-1)^e)/2 if p == 7,11,13,14 (mod 15).
Expansion of q*f(-q^3)f(-q^5)/(chi(-q)chi(-q^15)) in powers of q where f(),chi() are Ramanujan theta functions.
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PROG
| (PARI) a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-60, d)))
(PARI) {a(n)=if(n<1, 0, direuler(p=2, n, 1/(1-X)/(1-kronecker(-60, p)*X))[n])}
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)*eta(x^5+A)*eta(x^30+A)/eta(x+A)/eta(x^15+A), n))}
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CROSSREFS
| Sequence in context: A048622 A105661 * A121362 A091704 A175799 A123739
Adjacent sequences: A082448 A082449 A082450 * A082452 A082453 A082454
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Apr 25 2003
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