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 A088838 Numerator of the quotient sigma(3n)/sigma(n). 4

%I

%S 4,4,13,4,4,13,4,4,40,4,4,13,4,4,13,4,4,40,4,4,13,4,4,13,4,4,121,4,4,

%T 13,4,4,13,4,4,40,4,4,13,4,4,13,4,4,40,4,4,13,4,4,13,4,4,121,4,4,13,4,

%U 4,13,4,4,40,4,4,13,4,4,13,4,4,40,4,4,13,4,4,13,4,4,364,4,4,13,4,4,13,4,4,40

%N Numerator of the quotient sigma(3n)/sigma(n).

%H Robert Israel, <a href="/A088838/b088838.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Robert Israel_, Nov 19 2017: (Start)

%F a(n) = (3^(2+A007949(n))-1)/2.

%F G.f.: Sum_{k>=0} (3^(k+2)-1)*(x^(3^k)+x^(2*3^k))/(2*(1-x^(3^(k+1)))).

%F (End)

%p A088838 := proc(n)

%p numtheory[sigma](3*n)/numtheory[sigma](n) ;

%p numer(%) ;

%p end proc:

%p seq(A088838(n),n=1..100) ; # _R. J. Mathar_, Nov 19 2017

%p seq((3^(2+padic:-ordp(n,3))-1)/2, n=1..100); # _Robert Israel_, Nov 19 2017

%t k=3; Table[Numerator[DivisorSigma[1, k*n]/DivisorSigma[1, n]], {n, 1, 128}]

%o (PARI) a(n) = numerator(sigma(3*n)/sigma(n)) \\ _Felix FrÃ¶hlich_, Nov 19 2017

%Y Cf. A007949, A038712, A088837, A088839, A088840, A080278 (denominator), A000203.

%K easy,nonn,frac,look

%O 1,1

%A _Labos Elemer_, Nov 04 2003

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Last modified October 13 16:50 EDT 2019. Contains 327968 sequences. (Running on oeis4.)