A074754 - OEIS

%I #13 Apr 21 2023 21:21:04

%S 1,1,2,2,1,3,2,3,2,1,1,6,2,3,3,3,1,5,1,3,3,1,1,10,1,2,2,5,1,5,3,5,2,1,

%T 2,9,1,2,4,5,1,8,1,3,3,1,1,13,2,1,2,3,1,7,1,8,3,1,1,12,1,4,4,5,2,3,1,

%U 3,2,3,1,18,1,2,3,3,2,6,1,7,2,1,1,15,1,1,2,4,1,10,4,2,5,1,1,19,1,5,2,3,1

%N Number of integers k such that sigma(k) divides n.

%H Antti Karttunen, <a href="/A074754/b074754.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F sum(k=1, n, a(k)) seems to be asymptotic to c*n*log(n) with c=0.7...

%F G.f.: sum(k>=1, 1/(1-x^sigma(k))).

%F a(n) = Sum_{k=1..n} (1 - ceiling(n/sigma(k)) + floor(n/sigma(k))). - _Wesley Ivan Hurt_, Apr 21 2023

%t Table[Length[Select[Range[n], Divisible[n, DivisorSigma[1,#]]&]], {n, 1, 100}] (* _Vaclav Kotesovec_, Feb 16 2019 *)

%o (PARI) a(n)=sum(i=1,n,if(n%sigma(i),0,1))

%o (PARI) a(n)=if(n<1,0,polcoeff(sum(k=1,n,1/(1-x^sigma(k)),x*O(x^sigma(n))),n))

%Y Cf. A000203, A070610.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Sep 28 2002