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A080278
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a(n) = (3^(v_3(n) + 1) - 1)/2, where v_3(n) = highest power of 3 dividing n = A007949(n).
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12
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1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 40, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 40, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1, 121, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 1, 4, 1, 1, 4, 1, 1
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OFFSET
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1,3
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COMMENTS
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Denominator of the quotient sigma(3*n)/sigma(n). - Labos Elemer, Nov 04 2003
a(n) = b/(3*(c+d)) where b, c, d are the sums of the divisors of 3*n that are congruent respectively to 0, 1 and 2 mod 3. - Michel Lagneau, Nov 05 2012
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LINKS
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Table of n, a(n) for n=1..98.
Klaus Brockhaus, Illustration of A080278 and A080333
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FORMULA
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G.f.: Sum_{k>=0} 3^k*x^(3^k)/(1-x^(3^k)). - Ralf Stephan, Jun 15 2003
L.g.f.: -log(Product_{k>=0} (1 - x^(3^k))) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, Mar 15 2018
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EXAMPLE
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a(6) = 4 because the divisors of 3*6 = 18 are {1, 2, 3, 6, 9, 18} => b = 3 + 6 + 9 + 18 = 36, c = 1, d = 2, hence a(6) = b/(3*(c+d)) = 36/(3*(1+2)) = 36/9 = 4. - Michel Lagneau, Nov 05 2012
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MAPLE
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A080278 := n->(3^(A007949(n)+1)-1)/2;
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MATHEMATICA
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Table[Denominator[DivisorSigma[1, 3*n]/DivisorSigma[1, n]], {n, 1, 128}]
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PROG
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(PARI) a(n) = denominator(sigma(3*n)/sigma(n)); \\ Michel Marcus, Dec 15 2019
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CROSSREFS
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Cf. A007949, A080333, A088838 (numerator of sigma(3*n)/sigma(n)).
Sequence in context: A097322 A177023 A214333 * A258328 A070085 A131776
Adjacent sequences: A080275 A080276 A080277 * A080279 A080280 A080281
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KEYWORD
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nonn,mult,frac
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AUTHOR
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N. J. A. Sloane, Mar 19 2003
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STATUS
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approved
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