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 A087167 #31 Feb 16 2025 08:32:51
%S A087167 8925,32445,442365
%N A087167 Odd numbers such that sigma(n) - 2n = 6.
%C A087167 If m is in this sequence and 5 doesn't divide m then m is an odd Weird number. There are no other terms up to 2*10^9. _Jud McCranie_ wrote: There are no terms between 2*10^9 and 6.5*10^9.
%C A087167 a(4) > 10^12. - _Donovan Johnson_, Dec 08 2011
%C A087167 a(4) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C A087167 a(4) > 10^22. - _Wenjie Fang_, Jun 16 2014
%C A087167 Any term x of this sequence can be combined with any term y of A141548 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - _Timothy L. Tiffin_, Sep 13 2016
%D A087167 R. K. Guy, "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." B2 in Unsolved Problems in Number Theory, 2nd ed.New York:Springer- Verlag, pp. 45-53, 1994.
%H A087167 S. Benkoski, <a href="http://www.jstor.org/stable/2316276">Are All Weird Numbers Even?</a>, Problem E2308, Amer. Math. Monthly, 79 (7) (1972), 774.
%H A087167 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_233.htm">Puzzle 233. A little twist</a>.
%H A087167 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeirdNumber.html">Weird Number</a>.
%e A087167 a(1)=8925 because sigma(8925)=2*8925+6 and 8925 is the first odd number such that sigma(n)-2n=6.
%t A087167 Do[If[OddQ[n] && DivisorSigma[1, n] - 2n == 6, Print[n]], {n, 2*10^9}]
%o A087167 (PARI) is(n)=n%2 && sigma(n)==2*n+6 \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A087167 Cf. A003380, A077374, A005101, A005835, A141548 (deficiency 6).
%K A087167 hard,more,nonn,bref
%O A087167 1,1
%A A087167 _Farideh Firoozbakht_, Oct 19 2003