cp's OEIS Frontend

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.

A192287 Quasi-antiperfect numbers.

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%I A192287 #32 Feb 16 2025 08:33:15
%S A192287 11,12,21,111,979,19521,279259,4841411,7231219,10238379,14645479,
%T A192287 136531171,592994139,1869506239,13820158011,35242846899,211443753471,
%U A192287 330984643659,8806335754299
%N A192287 Quasi-antiperfect numbers.
%C A192287 A quasi-antiperfect number is a least anti-abundant number, i.e., one such that sigma*(n) = n+1, where sigma*(n) is the sum of the anti-divisors of n. Like quasi perfect numbers (see link) but using anti-divisors.
%C A192287 a(16) > 2*10^10. - _Donovan Johnson_, Sep 22 2011
%H A192287 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/QuasiperfectNumber.html">Quasiperfect number</a>
%e A192287 Anti-divisors of 979 are 2, 3, 19, 22, 103, 178, 653. Their sum is 980 and 980 = 979+1.
%p A192287 P:=proc(n)
%p A192287 local a,i,k;
%p A192287 for i from 3 to n do
%p A192287   a:=0;
%p A192287   for k from 2 to i-1 do
%p A192287     if abs((i mod k)-k/2)<1 then a:=a+k; fi;
%p A192287   od;
%p A192287   if i+1=a then print(i); fi;
%p A192287 od;
%p A192287 end:
%p A192287 P(1000000);
%o A192287 (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 A192287 isok(n) = sad(n) == n+1; \\ _Michel Marcus_, Oct 12 2019
%Y A192287 Cf. A066272, A073930, A192268, A192288.
%K A192287 nonn,more
%O A192287 1,1
%A A192287 _Paolo P. Lava_, Aug 02 2011
%E A192287 a(7)-a(15) from _Donovan Johnson_, Sep 22 2011
%E A192287 a(16)-a(18) by _Jud McCranie_, Aug 31 2019
%E A192287 a(19) by _Jud McCranie_, Oct 10 2019