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

1,2

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.

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.

Example

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

Crossrefs

Smaller than or equal to A214409.

Sequence in context: A360674 A324108 A324054 * A214409 A215509 A053480

Adjacent sequences: A214410 A214411 A214412 * A214414 A214415 A214416

Keyword

nonn

Author

Michel Marcus, Jul 22 2012

Status

approved