A192288 Almost anti-perfect numbers.

3, 4, 9, 19, 24, 131, 139, 339, 5881, 14849, 29501, 57169, 63061, 65789, 542781, 2439241, 3197249, 4111561, 8614481, 48657789, 218234169, 309296261, 731499089, 1191549689, 1569571661, 2471800109, 5687426561, 9505043161, 67784277581, 79468538969, 257067141569, 290324629889, 397393221689, 445568135041, 2260763053809

Offset: 1

Author

Paolo P. Lava, Aug 02 2011

Keywords

• nonn

Comments

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.

a(29) > 2*10^10. - Donovan Johnson, Sep 22 2011

Examples

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

Links

• Jud McCranie, Table of n, a(n) for n = 1..36
• Eric Weisstein's World of Mathematics, Almost perfect number

Crossrefs

Cf. A066272, A073930, A192267, A192287.

Programs

Maple

P:=proc(n)
local a,i,k;
for i from 3 to n do
  a:=0;
  for k from 2 to i-1 do
    if abs((i mod k)-k/2)<1 then a:=a+k; fi;
  od;
  if i-1=a then print(i); fi;
od;
end:
P(1000000);

Extensions

a(15)-a(28) from Donovan Johnson, Sep 22 2011

a(29)-a(34) from Jud McCranie, Aug 31 2019

a(35) from Jud McCranie, Sep 05 2019