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Search: id:A134080
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| A134080 |
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Expansion of ( f(-q^5)^5 / f(-q) + f(q^5)^5 / f(q) ) / 2 in powers of q^2 where f() is a Ramanujan theta function. |
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1
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| 1, 2, 5, 6, 7, 12, 12, 10, 16, 20, 12, 22, 25, 20, 30, 32, 24, 30, 36, 24, 42, 42, 35, 46, 43, 32, 52, 60, 40, 60, 62, 42, 60, 66, 44, 72, 72, 50, 72, 80, 61, 82, 80, 60, 90, 72, 64, 100, 96, 84, 102, 102, 60, 106, 110, 72, 112, 110, 84, 96, 133, 84, 125, 126, 84, 132, 120
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of ( phi(q^5) * psi(q^2) + q * phi(q) * psi(q^10) ) * f(-q^5) * phi(-q^5) / chi(-q) in powers of q where phi(), psi(), chi(), f() are Ramanujan theta functions.
a(n) = b(2*n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(5^e) = 5^e, b(p^e) = (p^(e+1) -1)/(p-1) if p == 1, 9 (mod 10), b(p^e) = (p^(e+1) +(-1)^e)/(p+1) if p == 3, 7 (mod 10).
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EXAMPLE
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q + 2*q^3 + 5*q^5 + 6*q^7 + 7*q^9 + 12*q^11 + 12*q^13 + 10*q^15 + 16*q^17 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, n = 2*n + 1 ; sumdiv(n, d, kronecker( 5, d) * n / d)) }
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CROSSREFS
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A053723(2*n) = A129303(2*n+1) = a(n).
Sequence in context: A023699 A058605 A103025 this_sequence A111300 A117548 A014489
Adjacent sequences: A134077 A134078 A134079 this_sequence A134081 A134082 A134083
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 07 2007
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