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%I #12 Apr 12 2024 03:55:16
%S 0,2,2,3,2,2,4,2,4,6,8,8,6,4,6,5,12,8,7,8,10,12,10,16,14,12,14,12,12,
%T 12,16,18,12,14,14,12,16,20,19,19,19,26,24,22,24,24,22,20,20,20,20,26,
%U 26,24,26,28,28,22,24,24,24,30,30,32,34,36,38,33,31,30,30,36,36,35,35,36,36,36,36,36,38,38,34,34
%N a(n) = Sum_{i=1..n} d(72*i+1) - Sum_{i=1..n} d(18*i+1), where d(n) = A000005(n).
%H Amiram Eldar, <a href="/A230296/b230296.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) = (2*log(2)/3) * n + O(n^(1/3)*log(n)). - _Amiram Eldar_, Apr 12 2024
%p See A230290.
%t Accumulate[Table[DivisorSigma[0, 72*n + 1] - DivisorSigma[0, 18*n + 1], {n, 1, 100}]] (* _Amiram Eldar_, Apr 12 2024 *)
%o (PARI) vector(100, n, sum(i=1, n, numdiv(72*i+1)) - sum(i=1, n, numdiv(18*i+1))) \\ _Michel Marcus_, Oct 09 2014
%Y Cf. A000005, A230290, A230291, A230292, A230293, A230294, A230295, A230476.
%K nonn,changed
%O 1,2
%A _N. J. A. Sloane_, Oct 17 2013
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