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

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