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A138191
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Denominator of (n-1)*n*(n+1)/12.
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4
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1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1
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OFFSET
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1,2
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COMMENTS
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Proof of 4-periodicity follows from evaluating (n+3)(n+4)(n+5)/12, subtracting (n-1)n(n+1)/12 and getting n^2+4n+5 which is an integer. - R. J. Mathar, Mar 07 2008
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LINKS
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FORMULA
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a(n) = 1 + (A000292(n-1) mod 2) = a(n-4).
O.g.f.: -1-5/(4(x-1))+1/(4(x+1))-1/(2(x^2+1)). (End)
Multiplicative with a(p^e) = 2 if p = 2 and e = 1, and 1 otherwise.
Dirichlet g.f.: zeta(s)*(1+1/2^s-1/4^s).
Sum_{k=1..n} a(k) ~ (5/4)*n. (End)
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EXAMPLE
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0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...
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MATHEMATICA
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Table[(n^3-n)/12, {n, 120}]//Denominator (* or *) PadRight[{}, 120, {1, 2, 1, 1}] (* Harvey P. Dale, Apr 15 2019 *)
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CROSSREFS
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KEYWORD
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nonn,frac,mult,easy
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AUTHOR
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STATUS
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approved
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