A192287 - OEIS

%I #31 Jul 19 2020 11:52:14

%S 11,12,21,111,979,19521,279259,4841411,7231219,10238379,14645479,

%T 136531171,592994139,1869506239,13820158011,35242846899,211443753471,

%U 330984643659,8806335754299

%N Quasi-antiperfect numbers.

%C 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 a(16) > 2*10^10. - _Donovan Johnson_, Sep 22 2011

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuasiperfectNumber.html">Quasiperfect number</a>

%e Anti-divisors of 979 are 2, 3, 19, 22, 103, 178, 653. Their sum is 980 and 980 = 979+1.

%p P:=proc(n)

%p local a,i,k;

%p for i from 3 to n do

%p   a:=0;

%p   for k from 2 to i-1 do

%p     if abs((i mod k)-k/2)<1 then a:=a+k; fi;

%p   od;

%p   if i+1=a then print(i); fi;

%p od;

%p end:

%p P(1000000);

%o (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 isok(n) = sad(n) == n+1; \\ _Michel Marcus_, Oct 12 2019

%Y Cf. A066272, A073930, A192268, A192288.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Aug 02 2011

%E a(7)-a(15) from _Donovan Johnson_, Sep 22 2011

%E a(16)-a(18) by _Jud McCranie_, Aug 31 2019

%E a(19) by _Jud McCranie_, Oct 10 2019