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A047789
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Denominators of Glaisher's I-numbers.
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6
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2, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 81, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 27, 1, 1, 3, 1, 1, 3, 1
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OFFSET
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0,1
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LINKS
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FORMULA
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For n >= 1, a(3*n) = a(3*n+2) = 1 and a(3*n+1) = 3*a(n).
G.f. g(x) satisfies g(x) = 3*x*g(x^3) + 2 - 3*x + (x^2+x^3)/(1-x^3). (End)
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EXAMPLE
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1/2, 1/3, 1, 7, 809/9, 1847, 55601, 6921461/3,...
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MAPLE
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f:= n -> 3^padic:-ordp(2*n+1, 3):
f(0):= 2:
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MATHEMATICA
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a[0] = 2; a[n_] := 3^IntegerExponent[2n+1, 3];
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PROG
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(PARI) a(n)=if(n<1, 2*(n==0), 3^valuation(2*n+1, 3)) /* Michael Somos, Feb 26 2004 */
(PARI) a(n)=if(n<1, 2*(n==0), n*=2; denominator(n!*polcoeff(3/(2+4*cos(x+O(x^n))), n))) /* Michael Somos, Feb 26 2004 */
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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