%I #8 May 19 2013 00:10:54
%S 1,3,5,33,60,245,304,372,1265,1568,1756,1799,1856,2409,2532,2976,3100,
%T 3281,3376,3394,3813,5637,5972,6147,6538,7213,7299,7896,7966,8371,
%U 10419,11526,13411,13856,14168,15024,15283,15709,16506,16577,16916,19212,19829,21372
%N Numbers n such that the sum of the numbers in the Collatz (3x+1) iteration of n is a perfect square.
%H Donovan Johnson, <a href="/A225866/b225866.txt">Table of n, a(n) for n = 1..1000</a>
%e 60 is in the sequence because 60 + 30 + 15 + 46 + 23 + 70 + 35 + 106 + 53 + 160 + 80 + 40 + 20 + 10 + 5 + 16 + 8 + 4 + 2 + 1 = 784 = 28^2.
%t collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]; Select[Range[22000], IntegerQ[Sqrt[Total[collatz[#]]]]&]
%Y Cf. A033493.
%K nonn
%O 1,2
%A _Michel Lagneau_, May 18 2013
