A192288 - OEIS

%I #42 Oct 23 2019 06:56:16

%S 3,4,9,19,24,131,139,339,5881,14849,29501,57169,63061,65789,542781,

%T 2439241,3197249,4111561,8614481,48657789,218234169,309296261,

%U 731499089,1191549689,1569571661,2471800109,5687426561,9505043161,67784277581,79468538969,257067141569,290324629889,397393221689,445568135041,2260763053809

%N Almost anti-perfect numbers.

%C An almost anti-perfect number is a least anti-deficient number, i.e., one such that sigma*(n)=n-1, where sigma*(n) is the sum of the anti-divisors of n. Like almost perfect numbers (see link) but using anti-divisors.

%C a(29) > 2*10^10. - _Donovan Johnson_, Sep 22 2011

%H Jud McCranie, <a href="/A192288/b192288.txt">Table of n, a(n) for n = 1..36</a>

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

%e Anti-divisors of 5881 are 2, 3, 9, 19, 619, 1307, 3921. Their sum is 5880 and 5880=5881-1.

%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);

%Y Cf. A066272, A073930, A192267, A192287.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Aug 02 2011

%E a(15)-a(28) from _Donovan Johnson_, Sep 22 2011

%E a(29)-a(34) from _Jud McCranie_, Aug 31 2019

%E a(35) from _Jud McCranie_, Sep 05 2019