A061869 Squares whose sum of digits as well as product of digits is a square (allowing zero).

0, 1, 4, 9, 100, 144, 400, 441, 900, 2025, 2304, 2601, 3600, 8100, 9025, 10000, 10201, 10404, 10609, 10816, 11025, 12100, 14400, 14884, 16900, 19600, 21904, 22500, 30625, 30976, 32400, 40000, 40401, 40804, 41209, 44100, 44944, 48400, 48841

Offset: 1

Author

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

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A061267 does not allow zero products.

Subsequence of A061867.

Programs

Maple

filter:= proc(t) local L;
  L:= convert(t,base,10);
  issqr(convert(L,`+`)) and issqr(convert(L,`*`))
end proc:
select(filter, [seq(i^2,i=0..300)]); # Robert Israel, Feb 15 2023

Mathematica

spdQ[n_]:=Module[{idn=IntegerDigits[n]},IntegerQ[Sqrt[Total[idn]]] && IntegerQ[ Sqrt[Times@@idn]]]; Select[Range[300]^2,spdQ] (* Harvey P. Dale, Jan 24 2013 *)