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

1,5

Links

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

Formula

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

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

Example

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.

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 *)

Prog

(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, ", "); ); }

Crossrefs

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

Sequence in context: A050925 A086696 A259743 * A241972 A357823 A226770

Adjacent sequences: A247012 A247013 A247014 * A247016 A247017 A247018

Keyword

nonn

Author

Michel Marcus, Sep 09 2014

Status

approved