A059047 Numbers x such that sigma(x)-x divides x-1, other than prime powers.

77, 611, 1073, 2033, 5293, 6031, 9983, 13969, 15947, 23489, 25241, 40301, 49901, 50249, 51101, 56759, 65017, 71677, 85079, 97217, 97783, 98099, 99101, 131237, 142091, 160133, 165101, 180767, 189281, 210367, 213053, 228719, 259741, 303239

Offset: 1

Author

Jud McCranie, Dec 18 2000

Keywords

• nonn

Comments

Primes and prime powers (A000961) also satisfy this equation. A059046 is the union of A000961 and A059047. These numbers are related to hyperperfect numbers (A034897) in the cited paper by te Riele.

Examples

			For x=77, sigma(77)=96, 96-77=19, which divides 77-1.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..5263 (terms < 10^11)
• H. J. J. te Riele, Rules for constructing hyperperfect numbers, Fibonacci Quarterly, 22(1)1984, 50-60. See equation (3), the set M*.

Crossrefs

Cf. A059046, A000203, A000961, A034897.

Programs

PARI

is(n)=n>1 && !isprimepower(n) && (n-1)%(sigma(n)-n)==0 \\ Charles R Greathouse IV, Oct 21 2015

Extensions

Offset corrected by Donovan Johnson, Nov 03 2011