login
Numbers n such that n^2 has property that the sum of its digits and the product of its digits are squares (allowing zeros).
3

%I #7 Dec 12 2013 15:56:25

%S 0,1,2,3,10,12,20,21,30,45,48,51,60,90,95,100,101,102,103,104,105,110,

%T 120,122,130,140,148,150,175,176,180,200,201,202,203,210,212,220,221,

%U 230,247,248,249,257,265,266,274,283,284,300,301,302,310,318,319,321

%N Numbers n such that n^2 has property that the sum of its digits and the product of its digits are squares (allowing zeros).

%H Harvey P. Dale, <a href="/A061868/b061868.txt">Table of n, a(n) for n = 1..1000</a>

%t spsQ[n_]:=Module[{idn2=IntegerDigits[n^2]},IntegerQ[Sqrt[Total[idn2]]] && IntegerQ[ Sqrt[Times@@idn2]]]; Select[Range[0,350],spsQ] (* _Harvey P. Dale_, Dec 12 2013 *)

%Y A061268 does not allow zero product of digits.

%K base,easy,nonn

%O 1,3

%A Larry Reeves (larryr(AT)acm.org), May 11 2001