A240746 - OEIS

%I #40 Jun 23 2015 10:57:46

%S 3,19,76,85,131,139,184,649,772,1010,1190,3234,3328,3649,3970,4181,

%T 5881,11748,13369,29501,65789,286544,830568,2035100,2405568,5152800,

%U 10515998,13343342,30232314,34729314,37548761,44933902,50637780,63919409

%N Numbers n>1 that divide the sum of their divisors and anti-divisors.

%C 1 and 2 have no anti-divisors.

%H Charles R Greathouse IV, <a href="/A240746/b240746.txt">Table of n, a(n) for n = 1..41</a>

%e The sum of the divisors of 772 is 1358 while the sum of its anti-divisors is 958. Then (1358 + 958) / 772 = 3.

%p with(numtheory); P:=proc(q) local a, j, k, n;

%p for n from 3 to q do k:=0; j:=n; while j mod 2 <> 1 do k:=k+1; j:=j/2; od;

%p a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;

%p if type((sigma(n)+a)/n,integer) then print(n); fi; od; end: P(10^9);

%o (PARI) is(n)=my(k=valuation(n,2));(sigma(2*n+1)+sigma(2*n-1)+sigma(n>>k)<<(k+1)+sigma(n))%n==2 \\ _Charles R Greathouse IV_, Jun 19 2015

%Y Cf. A000203, A066417.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Apr 23 2014

%E a(24)-a(34) from _Michel Marcus_, Jun 19 2015