A059046 Numbers n such that sigma(n)-n divides n-1.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 77, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211

Offset: 1

Author

Jud McCranie, Dec 18 2000

Keywords

• nonn

Comments

Primes and prime powers (A000961) satisfy this equation, but other numbers do also (A059047). This sequence is the union of A000961 and A059047. These are related to hyperperfect numbers (A034897) in the cited paper by te Riele. [Mentions this sequence]

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• JRM Antalan, JAB Dris, Some New Results On Even Almost Perfect Numbers Which Are Not Powers Of Two, arXiv preprint arXiv:1602.04248, 2016
• 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. A059047, A000203, A000961, A034897.

Programs

Magma

[n : n in [2..1000] | (n-1) mod (SumOfDivisors(n)-n) eq 0 ]; /* N. J. A. Sloane, Dec 23 2006 */

Mathematica

Select[Range[2,250],Divisible[#-1,DivisorSigma[1,#]-#]&] (* Harvey P. Dale, Jan 18 2011 *)

PARI

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