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 A218445 #25 Apr 20 2025 02:37:33
%S A218445 0,0,1,1,2,2,3,4,5,5,6,6,8,8,10,10,11,12,13,13,14,15,17,17,19,19,20,
%T A218445 21,23,23,24,24,26,26,28,29,31,32,33,33,34,34,37,37,39,39,40,41,43,44,
%U A218445 45,46,48,48,50,50,52,53,54,54,56,56,58,59,61,61,63,64,66,66,68,68,71,71,73,73,74,76,77,77,78
%N A218445 a(n) = Sum_{k>=0} floor(n/(5*k + 2)).
%H A218445 Seiichi Manyama, <a href="/A218445/b218445.txt">Table of n, a(n) for n = 0..10000</a>
%H A218445 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 A218445 a(n) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(2,5) - (1 - gamma)/5 = A256780 - (1 - A001620)/5 = 0.105832... (Smith and Subbarao, 1981). - _Amiram Eldar_, Apr 20 2025
%t A218445 Table[Sum[Floor[n/(5k+2)],{k,0,n}],{n,0,80}] (* _Harvey P. Dale_, Dec 08 2022 *)
%o A218445 (PARI) a(n)=sum(k=0,n\5,(n\(5*k+2)))
%o A218445 (Maxima) A218445[n]:=sum(floor(n/(5*k+2)),k,0,n)$
%o A218445 makelist(A218445[n],n,0,80); /* _Martin Ettl_, Oct 29 2012 */
%Y A218445 Partial sums of A001877.
%Y A218445 Cf. A218444, A218446, A218447.
%Y A218445 Cf. A001620, A256780.
%K A218445 nonn,easy
%O A218445 0,5
%A A218445 _Benoit Cloitre_, Oct 28 2012