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

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, 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, 9, 36, 29, 57, 0, 59, 31, 24, 14, 45, 9, 65, 22, 44, 13, 69, 1, 71

Offset: 1

Author

Michel Marcus, Sep 09 2014

Keywords

• nonn

Examples

			a(2) = 0, since below 2 no x have sigma(x)/x greater than sigma(2)/2.
a(3) = 1, since below 3 only sigma(2)/2 is greater than sigma(3)/3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203 (sigma), A017665 and A017666 (sigma(n)/n).

Programs

Mathematica

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 *)

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, ", "););}

Formula

a(n) = 0 if and only if n is superabundant (A004394).

a(p) = p - 2, for p prime.