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%I #12 Apr 12 2024 03:54:05
%S 1,1,2,6,6,8,6,6,11,9,13,15,14,18,20,18,14,19,21,21,25,21,25,31,33,33,
%T 31,29,33,36,32,32,34,40,40,42,41,37,49,51,51,49,47,51,52,54,50,54,54,
%U 58,60,52,56,64,62,66,68,64,68,74,72,68,73,75,75,75,77,77,85,83,79,77,72,84,88,88,84,92,94,90,98,90
%N a(n) = Sum_{i=1..n} d(24*i+9) - Sum_{i=1..n} d(6*i+3), where d(n) = A000005(n).
%H Amiram Eldar, <a href="/A230292/b230292.txt">Table of n, a(n) for n = 1..10000</a>
%H Jorge Luis Cimadevilla Villacorta, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.09.832">Certain inequalities associated with the divisor function</a>, Amer. Math. Monthly, 120 (2013), 832-837. (Shows that a(n) >= 0.)
%F a(n) = (5*log(2)/3) * n + O(n^(1/3)*log(n)). - _Amiram Eldar_, Apr 12 2024
%p See A230290.
%t Accumulate[Table[DivisorSigma[0, 24*n + 9] - DivisorSigma[0, 6*n + 3], {n, 1, 100}]] (* _Amiram Eldar_, Apr 12 2024 *)
%o (PARI) vector(100, n, sum(i=1, n, numdiv(24*i+9)) - sum(i=1, n, numdiv(6*i+3))) \\ _Michel Marcus_, Oct 09 2014
%Y Cf. A000005, A230290, A230291, A230293, A230294, A230295, A230296, A230476.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Oct 17 2013
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