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Search: id:A131099
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| A131099 |
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a(n) = n times number of divisors of n of form 3m+1 - n times number of divisors of form 3m+2. |
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+0
1
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| 1, 0, 3, 4, 0, 0, 14, 0, 9, 0, 0, 12, 26, 0, 0, 16, 0, 0, 38, 0, 42, 0, 0, 0, 25, 0, 27, 56, 0, 0, 62, 0, 0, 0, 0, 36, 74, 0, 78, 0, 0, 0, 86, 0, 0, 0, 0, 48, 147, 0, 0, 104, 0, 0, 0, 0, 114, 0, 0, 0, 122, 0, 126, 64, 0, 0, 134, 0, 0, 0, 0, 0, 146, 0, 75, 152, 0, 0, 158, 0, 81, 0, 0, 168, 0, 0
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(n) is multiplicative with a(3^e) = 3^e, a(p^e) = (e+1) *p^e if p=1 (mod 3), a(p^e) = (1+(-1)^e)/2 *p^e if p=2 (mod 3).
G.f. q*d/dq a(q)/6 where a() is the first cubic AGM analog function.
G.f.: (-1/2)* Sum_{u,v} u*v* x^(u*u +u*v +v*v) = Sum_k (3k+1)*x^(3k+1)/(1-x^(3k+1))^2.
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PROGRAM
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(PARI) {a(n)= if( n<1, 0, n* sumdiv(n, d, (d%3==1) -(d%3==2)))}
(PARI) {a(n)= local(A, p, e); if( n<1, 0, A=factor(n); n* prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==3, 1, if(p%3==1, e+1, !(e%2))))))}
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CROSSREFS
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n*A002324(n)=a(n).
Sequence in context: A025120 A025096 A086798 this_sequence A098800 A087666 A061353
Adjacent sequences: A131096 A131097 A131098 this_sequence A131100 A131101 A131102
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Jun 14 2007
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