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

1,1

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.

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*.

Example

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

Prog

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

Crossrefs

Cf. A059046, A000203, A000961, A034897.

Sequence in context: A020304 A154058 A027574 * A046149 A222728 A223649

Adjacent sequences: A059044 A059045 A059046 * A059048 A059049 A059050

Keyword

nonn

Author

Jud McCranie, Dec 18 2000

Extensions

Offset corrected by Donovan Johnson, Nov 03 2011

Status

approved