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

1,1

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

Links

Jud McCranie, Table of n, a(n) for n = 1..36

Eric Weisstein's World of Mathematics, Almost perfect number

Example

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

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);

Crossrefs

Cf. A066272, A073930, A192267, A192287.

Sequence in context: A304257 A217492 A178784 * A028344 A219680 A078010

Adjacent sequences: A192285 A192286 A192287 * A192289 A192290 A192291

Keyword

nonn

Author

Paolo P. Lava, Aug 02 2011

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

Status

approved