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A123477
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Expansion of (1-b(q))/3 in powers of q where b(q) is the second cubic AGM analog function.
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1
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1, 0, -2, 1, 0, 0, 2, 0, -2, 0, 0, -2, 2, 0, 0, 1, 0, 0, 2, 0, -4, 0, 0, 0, 1, 0, -2, 2, 0, 0, 2, 0, 0, 0, 0, -2, 2, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, -2, 3, 0, 0, 2, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, -4, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -2, 2, 0, 0, 2, 0, -2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| Moebius transform is period 9 sequence [ 1, -1, -3, 1, -1, 3, 1, -1, 0, ...].
a(n) is multiplicative and a(p^e) = -2 if p = 3 and e>0, a(p^e) = e+1 if p == 1 (mod 6), a(p^e) = (1+(-1)^e)/2 if p == 2, 5 (mod 6).
a(3n+2)=0. a(3n+1)=A033687(n), a(3n)=-2*A002324(n).
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PROG
| (PARI) {a(n)=if(n<1, 0, sumdiv(n, d, [ 0, 1, -1, -3, 1, -1, 3, 1, -1][d%9+1]))}
(PARI) {a(n)=local(A, p, e); if(n<1, 0, A=factor(n); prod( k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==3, -2, if(p%6==1, e+1, !(e%2))))))}
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CROSSREFS
| A005928(n)=-3a(n) if n>0. A113063(n)=|a(n)|.
Sequence in context: A176202 A040081 A113063 * A035225 A035219 A106347
Adjacent sequences: A123474 A123475 A123476 * A123478 A123479 A123480
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Sep 27 2006
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