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A080278 a(n) = (3^(v_3(n)+1)-1)/2, where v_3(n) = highest power of 3 dividing n = A007949(n). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Denominator of quotient = sigma(3n)/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

LINKS

Table of n, a(n) for n=1..98.

Klaus Brockhaus, Illustration of A080278 and A080333

FORMULA

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

EXAMPLE

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) = 36/(3(1+2)) = 36/9 = 4. - Michel Lagneau, Nov 05 2012

MAPLE

A080278 := n->(3^(A007949(n)+1)-1)/2;

MATHEMATICA

Table[Denominator[DivisorSigma[1, 3*n]/DivisorSigma[1, n]], {n, 1, 128}]

CROSSREFS

Cf. A007949, A080333.

Sequence in context: A097322 A177023 A214333 * A258328 A070085 A131776

Adjacent sequences:  A080275 A080276 A080277 * A080279 A080280 A080281

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Mar 19 2003

STATUS

approved

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)