%I
%S 440,28109312,79228362752
%N Numbers equal to the sum of their proper divisors d such that d mod 3 = 1.
%C 10^11 < a(4) <= 8581256320000.
%C The numbers equal to the sum of their proper divisors which are a multiple of 3 are the perfect numbers (A000396) multiplied by 3.
%e The proper divisors of 440 which are congruent to 1 mod 3 are 1, 4, 10, 22, 40, 55, 88, and 220. Since their sum is 440, 440 is a term.
%t Select[Range[5000], # == Plus @@ Select[Most@ Divisors@#, Mod[#,3] == 1 &] &]
%o (PARI) is(n)=sumdiv(n,d,if(d%3==1,d,0))==if(n%3==1,2*n,n) \\ _Charles R Greathouse IV_, May 09 2016
%Y Cf. A272715, A000396.
%K nonn,bref,more,hard
%O 1,1
%A _Giovanni Resta_, May 05 2016
