This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059046 #28 Jan 05 2025 19:51:36 %S A059046 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 A059046 61,64,67,71,73,77,79,81,83,89,97,101,103,107,109,113,121,125,127,128, %U A059046 131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211 %N A059046 Numbers n such that sigma(n)-n divides n-1. %C A059046 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 A059046 G. C. Greubel, <a href="/A059046/b059046.txt">Table of n, a(n) for n = 1..1000</a> %H A059046 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 A059046 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 A059046 For x=77, sigma(77)=96, 96-77=19, which divides 77-1. %t A059046 Select[Range[2,250],Divisible[#-1,DivisorSigma[1,#]-#]&] (* _Harvey P. Dale_, Jan 18 2011 *) %o A059046 (Magma) [n : n in [2..1000] | (n-1) mod (SumOfDivisors(n)-n) eq 0 ]; /* _N. J. A. Sloane_, Dec 23 2006 */ %o A059046 (PARI) is(n)=n>1 && (n-1)%(sigma(n)-n)==0 \\ _Charles R Greathouse IV_, Oct 21 2015 %Y A059046 Cf. A059047, A000203, A000961, A034897. %K A059046 nonn %O A059046 1,1 %A A059046 _Jud McCranie_, Dec 18 2000