%I #28 Jan 05 2025 19:51:36
%S 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,
%T 61,64,67,71,73,77,79,81,83,89,97,101,103,107,109,113,121,125,127,128,
%U 131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211
%N Numbers n such that sigma(n)-n divides n-1.
%C 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]
%H G. C. Greubel, <a href="/A059046/b059046.txt">Table of n, a(n) for n = 1..1000</a>
%H JRM Antalan, JAB Dris, <a href="http://arxiv.org/abs/1602.04248">Some New Results On Even Almost Perfect Numbers Which Are Not Powers Of Two</a>, arXiv preprint arXiv:1602.04248, 2016
%H H. J. J. te Riele, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/22-1/teriele.pdf">Rules for constructing hyperperfect numbers</a>, Fibonacci Quarterly, 22(1)1984, 50-60. See equation (3), the set M*.
%e For x=77, sigma(77)=96, 96-77=19, which divides 77-1.
%t Select[Range[2,250],Divisible[#-1,DivisorSigma[1,#]-#]&] (* _Harvey P. Dale_, Jan 18 2011 *)
%o (Magma) [n : n in [2..1000] | (n-1) mod (SumOfDivisors(n)-n) eq 0 ]; /* _N. J. A. Sloane_, Dec 23 2006 */
%o (PARI) is(n)=n>1 && (n-1)%(sigma(n)-n)==0 \\ _Charles R Greathouse IV_, Oct 21 2015
%Y Cf. A059047, A000203, A000961, A034897.
%K nonn
%O 1,1
%A _Jud McCranie_, Dec 18 2000