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Search: id:A112329
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| A112329 |
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Number of divisors of n if n odd, number of divisors of n/4 if n divisible by 4, otherwise 0. |
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+0
2
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| 1, 0, 2, 1, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 4, 3, 2, 0, 2, 2, 4, 0, 2, 4, 3, 0, 4, 2, 2, 0, 2, 4, 4, 0, 4, 3, 2, 0, 4, 4, 2, 0, 2, 2, 6, 0, 2, 6, 3, 0, 4, 2, 2, 0, 4, 4, 4, 0, 2, 4, 2, 0, 6, 5, 4, 0, 2, 2, 4, 0, 2, 6, 2, 0, 6, 2, 4, 0, 2, 6, 5, 0, 2, 4, 4, 0, 4, 4, 2, 0, 4, 2, 4, 0, 4, 8, 2, 0, 6, 3, 2, 0, 2, 4, 8
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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First occurrence of k: 2, 1, 3, 9, 15, 64, 45, 256, 96, 144, 192,4096, 240, ????, 768, 576, 480, ????, 720, ..., . (* Robert G. Wilson v *)
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FORMULA
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Multiplicative with a(2^e) = e-1 if e>0, a(p^e) = 1+e if p>2.
G.f.: Sum_{k>0} x^k/(1-(-x)^k) = Sum_{k>0} -(-x)^k/(1+(-x)^k). a(4n+2)=0.
Moebius transform is period 4 sequence [1, -1, 1, 1, ...].
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MATHEMATICA
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Rest[ CoefficientList[ Series[ Sum[x^k/(1 - (-x)^k), {k, 111}], {x, 0, 110}], x]] (from Robert G. Wilson v (rgwv(at)rgwv.com), Sep 20 2005)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, (-1)^n*sumdiv(n, d, (-1)^d))
(PARI) {a(n)=if(n<1, 0, if(n%2, numdiv(n), if(n%4, 0, numdiv(n/4))))} /* Michael Somos Sep 02 2006 */
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CROSSREFS
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A048272(n)=(-1)^(n-1)a(n). A099774(n)=a(2n-1). A000005(n)=a(4n). A000005(4n+1)=a(4n+1). A078703(n)=a(4n-1)/2.
Sequence in context: A055378 A029338 A048272 this_sequence A117448 A093321 A046144
Adjacent sequences: A112326 A112327 A112328 this_sequence A112330 A112331 A112332
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KEYWORD
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nonn,mult
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AUTHOR
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Michael Somos, Sep 04 2005
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