OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Marc Deléglise, Bounds for the density of abundant integers, Experiment. Math. Volume 7, Issue 2 (1998), 137-143.
Charles R. Wall, Phillip L. Crews and Donald B. Johnson, Density bounds for the sum of divisors function, Math. Comp. 26 (1972), 773-777.
Eric Weisstein's World of Mathematics, Abundant Number
FORMULA
a(n) ~ c*n, where c = 0.752380... is the asymptotic density of the deficient numbers (A318172). - Amiram Eldar, Mar 21 2021
EXAMPLE
For k=1 to 5, all numbers are deficients so a(k) = k in this range.
a(6) = 5 since 6 is the first number that is not deficient.
MATHEMATICA
a[n_]:=Length[Select[Range[n], DivisorSigma[1, #]/#<2&]]; a/@Range[68] (* Ivan N. Ianakiev, Apr 03 2015 *)
PROG
(PARI) a(n) = sum(k=1, n, sigma(k)/k < 2);
(Magma) [#[k:k in [1..n]| DivisorSigma(1, k) lt 2*k]:n in [1..70]]; // Marius A. Burtea, Nov 06 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 02 2015
STATUS
approved