A118489 Squares for which the product of the digits is a triangular number.

0, 1, 16, 25, 49, 100, 400, 576, 900, 1024, 1089, 1521, 1600, 2025, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 3025, 3600, 4096, 4900, 5041, 5625, 6084, 6400, 7056, 8100, 9025, 9409, 9604, 9801, 10000, 10201, 10404, 10609, 10816, 11025, 11236, 12100, 14400

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 05 2006

Keywords

• base
• nonn

Comments

Includes all squares not in A052041. - Robert Israel, May 25 2020

Examples

			26569 is in the sequence because (1) it is a square, (2) the product of its digits is 2*6*5*6*9=3240 which is a triangular number.
		

Links

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

Crossrefs

Cf. A000217, A052041.

Programs

Maple

filter:= n -> issqr(1+8*convert(convert(n,base,10),`*`)):
select(filter, [seq(i^2,i=1..1000)]); # Robert Israel, May 25 2020

Mathematica

Select[Range[0,120]^2,OddQ[Sqrt[8 (Times@@IntegerDigits[#]) +1]]&] (* Harvey P. Dale, Jul 06 2021 *)

Extensions

1600 inserted by Robert Israel, May 25 2020