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 A218447 #26 Apr 20 2025 02:38:02
%S A218447 0,0,0,0,1,1,1,1,2,3,3,3,4,4,5,5,6,6,7,8,9,9,9,9,11,11,11,12,14,15,15,
%T A218447 15,16,16,17,17,19,19,20,21,22,22,23,23,25,26,26,26,28,29,29,29,30,30,
%U A218447 32,32,34,35,36,37,38,38,38,39,41,41,41,41,43,44,45,45,48,48,49,49,51,51,52,53,54
%N A218447 a(n) = Sum_{k>=0} floor(n/(5*k + 4)).
%H A218447 Robert Israel, <a href="/A218447/b218447.txt">Table of n, a(n) for n = 0..10000</a>
%H A218447 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 A218447 a(n) = n*log(n)/5 + c*n + O(n^(1/3)*log(n)), where c = gamma(4,5) - (1 - gamma)/5 = A256849 - (1 - A001620)/5 = -0.213442... (Smith and Subbarao, 1981). - _Amiram Eldar_, Apr 20 2025
%p A218447 g:= n -> nops(select(t -> t mod 5 = 4, numtheory:-divisors(n))):
%p A218447 g(0):= 0:
%p A218447 ListTools:-PartialSums(map(g, [$0..100])); # _Robert Israel_, Apr 29 2021
%o A218447 (PARI) a(n)=sum(k=0,n,(n\(5*k+4)))
%o A218447 (Maxima) A218447[n]:=sum(floor(n/(5*k+4)),k,0,n)$
%o A218447 makelist(A218447[n],n,0,80); /* _Martin Ettl_, Oct 20 2012 */
%Y A218447 Partial sums of A001899.
%Y A218447 Cf. A218444, A218445, A218446.
%Y A218447 Cf. A001620, A256849.
%K A218447 nonn,easy
%O A218447 0,9
%A A218447 _Benoit Cloitre_, Oct 28 2012