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Search: id:A133691
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| A133691 |
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Expansion of (1 - ( phi(-q) * phi(q^2) )^2) / 4 in powers of q where phi() is a Ramanujan theta function. |
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+0
1
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| 1, -2, 4, -6, 6, -8, 8, -6, 13, -12, 12, -24, 14, -16, 24, -6, 18, -26, 20, -36, 32, -24, 24, -24, 31, -28, 40, -48, 30, -48, 32, -6, 48, -36, 48, -78, 38, -40, 56, -36, 42, -64, 44, -72, 78, -48, 48, -24, 57, -62, 72, -84, 54, -80, 72, -48, 80, -60, 60, -144, 62, -64, 104, -6, 84, -96, 68, -108, 96, -96, 72, -78
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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Expansion of (1 - ( eta(q)^2 * eta(q^4)^5 / ( eta(q^2)^3 * eta(q^8)^2 ) )^2) / 4 in powers of q.
a(n) is multiplicative with a(2) = -2, a(2^e) = -6 if e>1, a(p^e) = (p^(e+1) - 1) / (p - 1) if p>2.
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EXAMPLE
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q - 2*q^2 + 4*q^3 - 6*q^4 + 6*q^5 - 8*q^6 + 8*q^7 - 6*q^8 + 13*q^9 -...
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PROGRAM
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(PARI) {a(n) = if( n<1, 0, if( n%2, sigma(n), -2 * sumdiv(n/2, d, if(d%4, d))))}
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CROSSREFS
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-4 * A133690(n) = -(-1)^n * A111973(n) = a(n). -2 * A046897(n) = a(2*n). A008438(n) = a(2*n+1). -6 * A000593(n) = a(4*n). A112610(n) = a(4*n+1). 4 * A097723(n) = a(4*n+3).
Sequence in context: A131450 A114218 A111973 this_sequence A092517 A128558 A090346
Adjacent sequences: A133688 A133689 A133690 this_sequence A133692 A133693 A133694
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Sep 20 2007
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