A069077 Triangular numbers such that the product of digits is also a (positive) triangular number.

1, 3, 6, 66, 153, 231, 351, 465, 741, 1326, 2556, 5671, 6786, 14535, 21115, 24531, 25651, 33411, 43956, 57291, 58311, 71253, 92665, 95266, 123753, 153181, 167331, 278631, 325221, 341551, 351541, 372816, 459361, 491536, 516636, 521731, 567645, 572985, 613278

Offset: 1

Author

Amarnath Murthy, Apr 05 2002

Keywords

• nonn
• base

Links

• Amiram Eldar, Table of n, a(n) for n = 1..457

Crossrefs

Cf. A000217, A002473, A007954, A061380.

Programs

Magma

[m:m in [1..600000]|not 0 in Intseq(m) and IsSquare(8*m+1) and IsSquare(8*(&*Intseq(m))+1)]; // Marius A. Burtea, Aug 12 2019

Mathematica

aQ[n_] := (p = Times @@ IntegerDigits[n]) > 0 && IntegerQ @ Sqrt[8p + 1]; t[n_] := n(n+1)/2; Select[t[Range[10^3]], aQ] (* Amiram Eldar, Aug 12 2019 *)
Select[Accumulate[Range[1500]],FreeQ[IntegerDigits[#],0]&&OddQ[Sqrt[8 Times@@IntegerDigits[ #]+1]]&] (* Harvey P. Dale, May 01 2023 *)

Extensions

More terms from Jason Earls and Lior Manor, May 15 2002