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

1,3

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000217, A052041.

Sequence in context: A218439 A192689 A002644 * A110922 A065408 A112392

Adjacent sequences: A118486 A118487 A118488 * A118490 A118491 A118492

Keyword

base,nonn

Author

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

Extensions

1600 inserted by Robert Israel, May 25 2020

Status

approved