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A113241 a(n) = Sum_{k=1..n} (tau(2*k) - 1).

%I A113241 #15 Jun 16 2025 18:01:18
%S A113241 0,1,3,6,9,12,17,20,24,29,34,37,44,47,52,59,64,67,75,78,85,92,97,100,
%T A113241 109,114,119,126,133,136,147,150,156,163,168,175,186,189,194,201,210,
%U A113241 213,224,227,234,245,250,253,264,269,277,284,291,294,305,312,321,328
%N A113241 a(n) = Sum_{k=1..n} (tau(2*k) - 1).
%H A113241 Alois P. Heinz, <a href="/A113241/b113241.txt">Table of n, a(n) for n = 0..10000</a>
%F A113241 G.f.: (1/(1-x)) * Sum_{k>0} x^k*(1-x^(3*k))/((1-x^k)*(1-x^(2*k))).
%F A113241 a(n) = -n + Sum_{k=1..n} tau(2*k).
%p A113241 a:= proc(n) option remember; `if`(n<1, 0,
%p A113241       a(n-1)+numtheory[tau](2*n)-1)
%p A113241     end:
%p A113241 seq(a(n), n=0..57);  # _Alois P. Heinz_, Jun 16 2025
%t A113241 CoefficientList[ Series[ Sum[x^k(1 - x^(3k))/((1 - x^k)(1 - x^(2k))), {k, 60}], {x, 0, 57}]/(1 - x), x]
%Y A113241 Partial sums of A066660.
%Y A113241 Cf. A000005.
%K A113241 easy,nonn
%O A113241 0,3
%A A113241 _Paul Barry_, Oct 19 2005
%E A113241 More terms from _Robert G. Wilson v_, Oct 21 2005