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 A069928 #24 Dec 28 2024 09:17:22
%S A069928 1,1,2,2,3,4,5,5,5,5,6,6,7,8,9,9,10,10,11,12,13,14,15,15,15,15,16,16,
%T A069928 17,18,19,19,20,20,21,21,22,23,24,24,25,26,27,28,29,30,31,31,32,32,33,
%U A069928 33,34,35,36,37,38,38,39,40,41,42,42,42,43,44,45,46,47,48,49,49,50,50
%N A069928 Number of integers k, 1<=k<=n, such that tau(k) divides sigma(k) where tau(k) is the number of divisors of k and sigma(k) the sum of divisors of k.
%C A069928 Number of arithmetic numbers <= n, cf. A003601; partial sums of A245656. - _Reinhard Zumkeller_, Jul 28 2014
%H A069928 Reinhard Zumkeller, <a href="/A069928/b069928.txt">Table of n, a(n) for n = 1..10000</a>
%H A069928 Paul T. Bateman, Paul Erdős, Carl Pomerance, and E. G. Straus, <a href="https://doi.org/10.1007/BFb0096462">The arithmetic mean of the divisors of an integer</a>, in: Marvin I. Knopp (ed.), Analytic number theory, Proceedings of a Conference Held at Temple University, Philadelphia, May 12-15, 1980, Lecture Notes in Mathematics, Vol. 899, Springer-Verlag, 1981, pp. 197-220; <a href="https://math.dartmouth.edu/~carlp/PDF/31.pdf">alternative link</a>.
%H A069928 Amiram Eldar, <a href="/A069928/a069928.jpg">Plot of a(n)/n for n = 2^(10..33)</a>.
%H A069928 Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>.
%F A069928 a(n) = Card(k: 1<=k<=n : sigma(k) == 0 (mod tau(k))).
%F A069928 Limit_{n -> infinity} a(n)/n = C = 0.8...
%F A069928 Bateman et al. (1981) proved that the asymptotic density of the arithmetic numbers is 1. Therefore, the formula above is correct, but limit is C = 1. - _Amiram Eldar_, Dec 28 2024
%t A069928 Accumulate[Table[If[Divisible[DivisorSigma[1,n],DivisorSigma[0,n]],1,0],{n,80}]] (* _Harvey P. Dale_, Oct 06 2020 *)
%o A069928 (PARI) for(n=1,150,print1(sum(i=1,n,if(sigma(i)%numdiv(i),0,1)),","))
%o A069928 (Haskell)
%o A069928 a069928 n = a069928_list !! (n-1)
%o A069928 a069928_list = scanl1 (+) a245656_list
%o A069928 -- _Reinhard Zumkeller_, Jul 28 2014
%Y A069928 Cf. A000005, A000203, A003601, A245656.
%K A069928 easy,nonn
%O A069928 1,3
%A A069928 _Benoit Cloitre_, May 05 2002