A318172 Decimal expansion of the asymptotic density of deficient numbers.

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

Offset: 0

Author

Muniru A Asiru, Aug 20 2018

Keywords

• nonn
• cons
• more

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

Examples

			0.7523803...
		

Links

• 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.

Crossrefs

Cf. A005100, A302991, A303736.

Formula

Equals 1 - A302991.

Extensions

a(6) from Amiram Eldar, Aug 02 2025