%I #39 Mar 18 2022 10:46:40
%S 218,189648,720240,119967120,129705984,517941905,707902440,1321744320,
%T 98890370304,99080219520,119922568640,139834382688,347612467648,
%U 580542318720,952717920000,1064902900320,1153644808680,2255573174400,3903820736256,6859688278905,10944640212480,14424196864000
%N Numbers n such that sigma(x) - x = n has at least two solutions, with each x having the same squarefree kernel, where sigma(x) is the sum of divisor function (A000203).
%C Numbers n such that n = A001065(j) = A001065(k) and A007947(j) = A007947(k), where j != k.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_774.htm">Prime Puzzle 774. S(i) and Rad(i)</a>, The Prime Puzzles and Problems Connection.
%e 218 is the sum of proper divisors of 250 and 160, and rad(250) = rad(160) = 10, hence 218 is in the sequence with j=250 and k=160.
%e Other examples of n and j, k:
%e For n = 189648, j = 95832, k = 85536.
%e For n = 720240, j = 288120, k = 246960.
%e For n = 119967120, j = 38755080, k = 34398000.
%e For n = 129705984, j = 71614464, k = 60424704.
%Y Cf. A001065 (sum of proper divisors of n), A007947 (squarefree kernel of n).
%Y Cf. A048138, A152454, A254035.
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Dec 25 2014
%E a(6) onward from _Fred Schneider_, Feb 07 2015