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Search: id:A082451
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| A082451 |
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Sum over divisors d of n of Kronecker symbol (-60,d). |
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+0
4
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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; listen)
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OFFSET
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1,17
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COMMENT
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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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FORMULA
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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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PROGRAM
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(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
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Sequence in context: A073781 A048622 A105661 this_sequence A121362 A091704 A123739
Adjacent sequences: A082448 A082449 A082450 this_sequence A082452 A082453 A082454
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Apr 25 2003
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