This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218446 #24 Apr 20 2025 02:37:45
%S A218446 0,0,0,1,1,1,2,2,3,4,4,4,5,6,6,7,8,8,10,10,10,11,11,12,14,14,15,16,17,
%T A218446 17,18,18,19,21,21,21,23,23,24,26,27,27,28,29,29,30,31,31,34,34,34,35,
%U A218446 36,37,39,39,41,42,43,43,44,44,44,46,47,48,50,50,51,53,53,53,56,57,57,58,59,59,62,62,63
%N A218446 a(n) = Sum_{k>=0} floor(n/(5*k + 3)).
%H A218446 Seiichi Manyama, <a href="/A218446/b218446.txt">Table of n, a(n) for n = 0..10000</a>
%H A218446 R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
%F A218446 a(n) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,5) - (1 - gamma)/5 = A256848 - (1 - A001620)/5 = -0.0983206... (Smith and Subbarao, 1981). - _Amiram Eldar_, Apr 20 2025
%t A218446 Accumulate[Table[Count[Divisors[n],_?(Mod[#,5]==3&)],{n,0,90}]] (* _Harvey P. Dale_, Nov 08 2012 *)
%o A218446 (PARI) a(n)=sum(k=0,n,(n\(5*k+3)))
%o A218446 (Maxima) A218446[n]:=sum(floor(n/(5*k+3)),k,0,n)$
%o A218446 makelist(A218446[n],n,0,80); /* _Martin Ettl_, Oct 29 2012 */
%Y A218446 Partial sums of A001878.
%Y A218446 Cf. A218444, A218445, A218447.
%Y A218446 Cf. A001620, A256848.
%K A218446 nonn,easy
%O A218446 0,7
%A A218446 _Benoit Cloitre_, Oct 28 2012