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%I #17 Feb 16 2019 08:06:38
%S 0,1,1,2,3,3,4,5,6,6,6,6,8,9,10,11,11,11,13,13,14,14,14,14,17,17,17,
%T 17,18,18,19,21,23,23,23,23,24,24,25,26,27,27,30,30,31,31,31,31,34,34,
%U 34,34,34,34,36,36,38,39,39,39,42,42,43,44,44,44,44,44,45,45,45,45,50,50
%N Number of integers k such that sigma(k) < n.
%H Robert Israel, <a href="/A074753/b074753.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = card( k : sigma(k) < n ); a(n) is asymptotic to c*n with c=0.67...
%p N:= 100: # to get a(1)..a(N)
%p V:= Vector(N):
%p for n from 1 to N-2 do
%p s:= numtheory:-sigma(n)+1;
%p if s <= N then V[s]:= V[s]+1 fi;
%p od:
%p ListTools:-PartialSums(V); # _Robert Israel_, Jan 08 2018
%t Table[Length[Select[Range[n], DivisorSigma[1,#] < n&]], {n, 1, 100}] (* _Vaclav Kotesovec_, Feb 16 2019 *)
%o (PARI) a(n)=sum(i=1,n,if(1+sign(sigma(i)-n),0,1))
%Y Partial sums of A054973.
%Y Cf. A000203.
%K nonn
%O 1,4
%A _Benoit Cloitre_, Sep 28 2002
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