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A059046
Numbers n such that sigma(n)-n divides n-1.
2
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
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
KEYWORD
nonn
AUTHOR
Jud McCranie, Dec 18 2000
STATUS
approved