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%I #21 Apr 12 2024 03:53:48
%S 0,2,2,2,0,2,4,6,6,4,4,4,6,6,6,6,10,10,10,10,10,12,10,10,8,6,12,14,16,
%T 16,16,18,16,18,16,14,16,16,16,12,18,22,22,24,20,22,22,24,22,20,22,28,
%U 26,26,26,24,26,26,26,26,24,28,30,30,30,30,34,34,36,32,32,32,34,36,32,34,36,34,34,34,36,36,40,42
%N a(n) = Sum_{i=1..n} d(24*i+17) - Sum_{i=1..n} d(6*i+5), where d(n) = A000005(n).
%H Robert Israel, <a href="/A230291/b230291.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, 24*n + 17] - DivisorSigma[0, 6*n + 5], {n, 1, 100}]] (* _Amiram Eldar_, Apr 12 2024 *)
%o (PARI) vector(100, n, sum(i=1, n, numdiv(24*i+17)) - sum(i=1, n, numdiv(6*i+5))) \\ _Michel Marcus_, Oct 09 2014
%o (Magma) [&+[#Divisors(24*i+17):i in [1..n]]- &+[#Divisors(6*i+5):i in [1..n]]:n in [1..90]]; // _Marius A. Burtea_, Jan 03 2020
%Y Cf. A000005, A230290, A230292, A230293, A230294, A230295, A230296, A230476.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 17 2013
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