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%I #17 Sep 23 2020 02:48:01
%S 1,5,13,41,97,305,793,2393,6853,20405,60073,179957,535537,1604165,
%T 4799821,14386649,43112257,129286385,387682633,1162827737,3487836469,
%U 10462571525,31385253913,94151940581,282446314993,847323239045,2541932965741,7625734923497,22877060890417
%N Dirichlet convolution of b_n=2^(n-1) with c_n=3^(n-1).
%H Robert Israel, <a href="/A034735/b034735.txt">Table of n, a(n) for n = 1..2094</a>
%F a(n) ~ 3^(n-1). - _Vaclav Kotesovec_, Sep 11 2019
%F G.f.: Sum_{k>=1} 3^(k-1)*x^k / (1 - 2*x^k). - _Ilya Gutkovskiy_, Sep 22 2020
%p f:= n -> add(2^d * 3^(n/d)/6, d = numtheory:-divisors(n)):
%p map(f, [$1..50]); # _Robert Israel_, Jun 25 2020
%t Table[Sum[2^(d - 1)*3^(n/d - 1), {d, Divisors[n]}], {n, 1, 30}] (* _Vaclav Kotesovec_, Sep 11 2019 *)
%o (PARI) a(n) = sumdiv(n,d, 2^(d-1) * 3^(n/d-1) ); /* _Joerg Arndt_, Apr 14 2013 */
%Y Cf. A038039.
%K nonn
%O 1,2
%A _Erich Friedman_
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