A214413 a(n) is the smallest m such that the irreducible fraction m/n is not an abundancy outlaw.

1, 3, 4, 7, 6, 13, 8, 15, 13, 19, 12, 29, 14, 25, 26, 31, 18, 41, 20, 47, 32, 37, 24, 65, 31, 43, 40, 57, 30, 73, 32, 63, 50, 55, 48, 91, 38, 61, 56, 93, 42, 97, 44, 85, 82, 73, 48, 125, 57, 93, 74, 99, 54, 121, 72, 125, 80, 91, 60, 169, 62, 97, 104, 127, 84

Offset: 1

Author

Michel Marcus, Jul 22 2012

Keywords

• nonn

Comments

The theorem on page 7 of Stanton and Holdener gives conditions for a rational to be an abundancy outlaw.

For a given n, these conditions have been checked by starting with m/n=sigma(n)/n and then increasing m until they fail.

Examples

			a(3) = 4 because 4/3 is the abundancy index of 3, so 4/3 is not an abundancy outlaw.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000
• William G. Stanton and Judy A. Holdener, Abundancy "Outlaws" of the Form (sigma(N) + t)/N, Journal of Integer Sequences , Vol 10 (2007) , Article 07.9.6.

Crossrefs

Smaller than or equal to A214409.