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%I #14 Oct 06 2020 14:01:43
%S 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 17,18,19,19,20,20,21,21,22,23,24,24,25,26,27,28,29,30,31,31,32,32,33,
%U 33,34,35,36,37,38,38,39,40,41,42,42,42,43,44,45,46,47,48,49,49,50,50
%N Number of k, 1<=k<=n, such that tau(k) divides sigma(k) where tau(x) is the number of divisors of x and sigma(x) the sum of divisors of x.
%C Number of arithmetic numbers <= n, cf. A003601; partial sums of A245656. - _Reinhard Zumkeller_, Jul 28 2014
%H Reinhard Zumkeller, <a href="/A069928/b069928.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>
%F a(n)=Card(k: 1<=k<=n : sigma(k) == 0 (mod tau(k) ) : lim n -> infinity a(n)/n=C=0, 8...
%t Accumulate[Table[If[Divisible[DivisorSigma[1,n],DivisorSigma[0,n]],1,0],{n,80}]] (* _Harvey P. Dale_, Oct 06 2020 *)
%o (PARI) for(n=1,150,print1(sum(i=1,n,if(sigma(i)%numdiv(i),0,1)),","))
%o (Haskell)
%o a069928 n = a069928_list !! (n-1)
%o a069928_list = scanl1 (+) a245656_list
%o -- _Reinhard Zumkeller_, Jul 28 2014
%Y Cf. A000005, A000203, A003601, A245656.
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, May 05 2002
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