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%I #17 Apr 12 2024 03:17:34
%S 0,1,1,0,2,3,1,3,3,1,5,5,3,5,5,5,5,5,5,8,10,6,8,7,5,11,9,7,11,12,10,
%T 10,12,10,12,14,10,12,12,11,17,16,14,16,14,14,18,18,14,16,18,14,16,18,
%U 18,25,23,19,19,18,20,20,22,20,24,24,18,24,24,22,26,25,21,27,29,27,27,27,25,25,29,25,29,28,26,32
%N a(n) = Sum_{i=1..n} d(4*i+1) - Sum_{i=1..n} d(2*i+1), where d(n) = A000005(n).
%H Amiram Eldar, <a href="/A230294/b230294.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) = A230476(n) - A230293(n). - _Jonathan Sondow_, Oct 20 2013
%F a(n) = (log(2)/2) * n + O(n^(1/3)*log(n)). - _Amiram Eldar_, Apr 12 2024
%p See A230290.
%t Accumulate[Table[DivisorSigma[0, 4*n + 1] - DivisorSigma[0, 2*n + 1], {n, 1, 100}]] (* _Amiram Eldar_, Apr 12 2024 *)
%o (PARI) vector(100, n, sum(i=1, n, numdiv(4*i+1)) - sum(i=1, n, numdiv(2*i+1))) \\ _Michel Marcus_, Oct 09 2014
%Y Cf. A000005, A230290, A230291, A230292, A230293, A230295, A230296, A230476.
%K nonn,changed
%O 1,5
%A _N. J. A. Sloane_, Oct 17 2013
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