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

1,1

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]

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*.

Example

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

Mathematica

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

Prog

(Magma) [n : n in [2..1000] | (n-1) mod (SumOfDivisors(n)-n) eq 0 ]; /* N. J. A. Sloane, Dec 23 2006 */
(PARI) is(n)=n>1 && (n-1)%(sigma(n)-n)==0 \\ Charles R Greathouse IV, Oct 21 2015

Crossrefs

Cf. A059047, A000203, A000961, A034897.

Sequence in context: A326645 A371445 A325371 * A363727 A329366 A144711

Adjacent sequences: A059043 A059044 A059045 * A059047 A059048 A059049

Keyword

nonn

Author

Jud McCranie, Dec 18 2000

Status

approved