%I #6 Nov 21 2013 12:48:14

%S 27,33,45,57,69,81,105,117,141,177,189,225,249,261,285,321,357,369,

%T 405,429,441,477,501,537,585,609,621,645,657,681,765,789,825,837,897,

%U 909,945,981,1005,1041,1077,1089,1149,1161,1185,1197,1269,1341,1365,1377

%N Doubly (3)-perfect numbers.

%C We define a doubly (r)-perfect number n as one for which Sum[d; 1<=d<n, n mod d=r] = 2n. It appears that all differences, a(n+1)-a(n), of consecutive (3)-perfect numbers are multiples of 6.

%H Harvey P. Dale, <a href="/A088499/b088499.txt">Table of n, a(n) for n = 1..500</a>

%e 27 is a (3)-perfect number since the integers d in 1..26 for which 27 mod d=3 are 4, 6, 8, 12 and 24 and these sum to 54=2*27.

%t d3pnQ[n_]:=Total[Select[Range[n-1],Mod[n,#]==3&]]==2 n; Select[Range[1400],d3pnQ] (* _Harvey P. Dale_, May 15 2012 *)

%K nonn

%O 1,1

%A _John W. Layman_, Nov 11 2003