A318172 Decimal expansion of the asymptotic density of deficient numbers.

7, 5, 2, 3, 8, 0, 3

Offset

0,1

Comments

A number n is abundant if sigma(n) > 2n, perfect if sigma(n) = 2n, deficient if sigma(n) < 2n, where sigma(n) is the sum of the divisors of n. Since the asymptotic density of the perfect numbers is 0, the asymptotic density of the deficient numbers (0.752380...) + the asymptotic density of the abundant numbers (0.247619...) is 1. - Muniru A Asiru, Oct 13 2018

Links

Table of n, a(n) for n=0..6.

Peter Gerralld Banda, The Schnirelmann density of the set of deficient numbers, Thesis, California State Polytechnic University, Pomona, 2015.

Nathan McNew and Jai Setty, On the densities of covering numbers and abundant numbers, arXiv:2507.23041 [math.NT], 2025.

Formula

Equals 1 - A302991.

Example

0.7523803...

Crossrefs

Cf. A005100, A302991, A303736.

Sequence in context: A071876 A306538 A191503 * A070404 A258370 A135537

Adjacent sequences: A318169 A318170 A318171 * A318173 A318174 A318175

Keyword

nonn,cons,more

Author

Muniru A Asiru, Aug 20 2018

Extensions

a(6) from Amiram Eldar, Aug 02 2025

Status

approved