A192287 Quasi-antiperfect numbers.

11, 12, 21, 111, 979, 19521, 279259, 4841411, 7231219, 10238379, 14645479, 136531171, 592994139, 1869506239, 13820158011, 35242846899, 211443753471, 330984643659, 8806335754299

Offset

1,1

Comments

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.

a(16) > 2*10^10. - Donovan Johnson, Sep 22 2011

Links

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, Quasiperfect number

Example

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

Prog

(PARI) sad(n) = vecsum(select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n)))); \\ A066417
isok(n) = sad(n) == n+1; \\ Michel Marcus, Oct 12 2019

Crossrefs

Cf. A066272, A073930, A192268, A192288.

Sequence in context: A098752 A240763 A231871 * A084855 A367612 A367340

Adjacent sequences: A192284 A192285 A192286 * A192288 A192289 A192290

Keyword

nonn,more

Author

Paolo P. Lava, Aug 02 2011

Extensions

a(7)-a(15) from Donovan Johnson, Sep 22 2011

a(16)-a(18) by Jud McCranie, Aug 31 2019

a(19) by Jud McCranie, Oct 10 2019

Status

approved