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 A073930 #65 Apr 16 2025 05:26:17 %S A073930 5,8,41,56,946,5186,6874,8104,17386,27024,84026,167786,2667584, %T A073930 4921776,27914146,505235234,3238952914,73600829714,455879783074, %U A073930 528080296234,673223621664,4054397778846,4437083907194,4869434608274,6904301600914,7738291969456 %N A073930 Numbers that are equal to the sum of their anti-divisors. %C A073930 See A066272 for definition of anti-divisor. %H A073930 Jon Perry, <a href="https://web.archive.org/web/20060923020024/http://www.users.globalnet.co.uk/~perry/maths/antiperfect.htm">Anti-perfects, anti-amicables and other records</a>. %e A073930 For k=5186, the anti-divisor sum: 3+4+11+23+41+253+451+943+3457 = 5186. %o A073930 (Python) %o A073930 from sympy import divisors %o A073930 A073930 = [n for n in range(1,10**5) if sum([2*d for d in divisors(n) if n > 2*d and n % (2*d)] + [d for d in divisors(2*n-1) if n > d >=2 and n % d] + [d for d in divisors(2*n+1) if n > d >=2 and n % d]) == n] # _Chai Wah Wu_, Aug 14 2014 %o A073930 (PARI) sad(n) = vecsum(select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n)))); \\ A066417 %o A073930 isok(n) = sad(n) == n; \\ _Michel Marcus_, Oct 12 2019 %Y A073930 Cf. A066417, A192272. %K A073930 nonn %O A073930 1,1 %A A073930 _Jason Earls_, Sep 03 2002 %E A073930 a(16)-a(17) from _Lior Manor_, Mar 03 2004 %E A073930 a(18) from _Donovan Johnson_, Jun 19 2010 %E A073930 a(19)-a(21) by _Jud McCranie_, Aug 31 2019 %E A073930 a(22)-a(26) by _Jud McCranie_, Oct 10 2019