cp's OEIS Frontend

A247015 Number of integers x smaller than n and that satisfy sigma(x)/x > sigma(n)/n where sigma is the sum of divisors.

%I A247015 #9 Jul 01 2019 07:56:08
%S A247015 0,0,1,0,3,0,5,1,4,2,9,0,11,5,6,2,15,1,17,2,10,9,21,0,16,11,15,4,27,1,
%T A247015 29,7,19,16,22,0,35,18,24,4,39,4,41,12,16,23,45,0,35,15,32,14,51,7,37,
%U A247015 9,36,29,57,0,59,31,24,14,45,9,65,22,44,13,69,1,71
%N A247015 Number of integers x smaller than n and that satisfy sigma(x)/x > sigma(n)/n where sigma is the sum of divisors.
%H A247015 Amiram Eldar, <a href="/A247015/b247015.txt">Table of n, a(n) for n = 1..10000</a>
%F A247015 a(n) = 0 if and only if n is superabundant (A004394).
%F A247015 a(p) = p - 2, for p prime.
%e A247015 a(2) = 0, since below 2 no x have sigma(x)/x greater than sigma(2)/2.
%e A247015 a(3) = 1, since below 3 only sigma(2)/2 is greater than sigma(3)/3.
%t A247015 r[n_] := r[n] := DivisorSigma[1,n]/n; a[n_] := Module[{rn = r[n]}, Count[Range[n-1], _?(r[#] > rn &)]]; Array[a, 73] (* _Amiram Eldar_, Jul 01 2019 *)
%o A247015 (PARI) lista(nn) = {v = vector(nn, n, sigma(n)/n); for (n=1, nn, nb = sum(i=1, n, v[i] > v[n]); print1(nb, ", "););}
%Y A247015 Cf. A000203 (sigma), A017665 and A017666 (sigma(n)/n).
%K A247015 nonn
%O A247015 1,5
%A A247015 _Michel Marcus_, Sep 09 2014