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 A141548 #43 Sep 08 2022 08:45:35
%S A141548 7,15,52,315,592,1155,2102272,815634435
%N A141548 Numbers n whose deficiency is 6.
%C A141548 a(9) > 10^12. - _Donovan Johnson_, Dec 08 2011
%C A141548 a(9) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C A141548 a(9) > 10^18. - _Hiroaki Yamanouchi_, Aug 21 2018
%C A141548 For all k in A059242, the number m = 2^(k-1)*(2^k+5) is in this sequence. This yields further terms 2^46*(2^47+5), 2^52*(2^53+5), 2^140*(2^141+5), ... All even terms known so far and the initial 7 = 2^0*(2^1+5) are of this form. All odd terms beyond a(2) are of the form a(n) = a(k)*p*q, k < n. We have proved that there is no further term of this form with the a(k) given so far. - _M. F. Hasler_, Apr 23 2015
%C A141548 A term n of this sequence multiplied by a prime p not dividing it is abundant if and only if p < sigma(n)/6 = n/3-1. For the even terms 592 and 2102272, there is such a prime near this limit (191 resp. 693571) such that n*p is a primitive weird number, cf. A002975. For a(3)=52, the largest such prime, 11, is already too small. Odd weird numbers do not exist within these limits. - _M. F. Hasler_, Jul 19 2016
%C A141548 Any term x of this sequence can be combined with any term y of A087167 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
%H A141548 Gianluca Amato, Maximilian Hasler, Giuseppe Melfi, Maurizio Parton, <a href="https://arxiv.org/abs/1803.00324">Primitive weird numbers having more than three distinct prime factors</a>, Riv. Mat. Univ. Parma, 7(1), (2016), 153-163, arXiv:1803.00324 [math.NT], 2018.
%e A141548 a(1) = 7, since 2*7 - sigma(7) = 14 - 8 = 6. - _Timothy L. Tiffin_, Sep 13 2016
%t A141548 lst={};Do[If[n==Plus@@Divisors[n]-n+6,AppendTo[lst,n]],{n,10^4}];Print[lst];
%t A141548 Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 6 &] (* _Vincenzo Librandi_, Sep 14 2016 *)
%o A141548 (PARI) is(n)=sigma(n)==2*n-6 \\ _Charles R Greathouse IV_, Apr 23 2015, corrected by _M. F. Hasler_, Jul 18 2016
%o A141548 (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -6]; // _Vincenzo Librandi_, Sep 14 2016
%Y A141548 Cf. A087485 (odd terms).
%Y A141548 Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141549 (deficiency 12), A141550 (deficiency 14), A125248 (deficiency 16), A223608 (deficiency 18), A223607 (deficiency 20).
%Y A141548 Cf. A087167 (abundance 6).
%K A141548 nonn,more,hard
%O A141548 1,1
%A A141548 _Vladimir Joseph Stephan Orlovsky_, Aug 16 2008
%E A141548 a(8) from _Donovan Johnson_, Dec 08 2011