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 A218444 #24 Apr 20 2025 02:37:12
%S A218444 0,1,2,3,4,5,7,8,9,10,11,13,15,16,17,18,20,21,23,24,25,27,29,30,32,33,
%T A218444 35,36,37,38,40,42,44,46,47,48,51,52,53,54,55,57,60,61,63,64,66,67,70,
%U A218444 71,72,74,76,77,79,81,83,84,85,86,88,90,92,94,96,97,101,102,103,104,105
%N A218444 a(n) = Sum_{k>=0} floor(n/(5*k + 1)).
%H A218444 Seiichi Manyama, <a href="/A218444/b218444.txt">Table of n, a(n) for n = 0..10000</a>
%H A218444 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 A218444 a(n) = Sum_{k>=0} floor(n/(5*k + 1)).
%F A218444 a(n) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(1,5) - (1 - gamma)/5 = A256779 - (1 - A001620)/5 = 0.651363... (Smith and Subbarao, 1981). - _Amiram Eldar_, Apr 20 2025
%t A218444 a[n_] := Sum[ Floor[n/(5*k+1)], {k, 0, Ceiling[n/5]}]; Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, Feb 22 2013 *)
%o A218444 (PARI) a(n)=sum(k=0,n,(n\(5*k+1)))
%o A218444 (Maxima) A218444[n]:=sum(floor(n/(5*k+1)),k,0,n)$
%o A218444 makelist(A218444[n],n,0,80); /* _Martin Ettl_, Oct 29 2012 */
%Y A218444 Partial sums of A001876.
%Y A218444 Cf. A218444, A218445, A218446.
%Y A218444 Cf. A001620, A256779.
%K A218444 nonn,easy
%O A218444 0,3
%A A218444 _Benoit Cloitre_, Oct 28 2012