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1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3, 1, 1, 6, 1, 1, 3, 4, 1, 3, 1, 2, 3, 1, 1, 12, 1, 1, 3, 2, 1, 3, 1, 4, 3
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OFFSET
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1,3
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COMMENTS
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Twice connected to Bernoulli numbers A164555/A027642 via the Akiyama-Tanigawa algorithm.
Conjecture (checked for the first 3000 entries): periodic with a(n+24)=a(n).
Is this a multiplicative function?
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LINKS
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FORMULA
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Multiplicative with a(2^3) = 2^min(e-1,2), a(3^e) = 3, and a(p^e) = 1 for a prime p >= 5.
Dirichlet g.f.: zeta(s) * (1 + 1/2^(2*s) + 1/2^(3*s-1)) * (1 + 2/3^s).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 5/2. (End)
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MAPLE
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b := proc(n) n/(n+1)/(n+2) ; end: A051712 := proc(n) numer( b(n)-b(n+1)) ; end:
A026741 := proc(n) if type(n, 'odd') then n; else n/2; fi; end:
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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