A069077 - OEIS

%I #24 Sep 25 2024 15:24:08

%S 1,3,6,66,153,231,351,465,741,1326,2556,5671,6786,14535,21115,24531,

%T 25651,33411,43956,57291,58311,71253,92665,95266,123753,153181,167331,

%U 278631,325221,341551,351541,372816,459361,491536,516636,521731,567645,572985,613278

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

%H Amiram Eldar, <a href="/A069077/b069077.txt">Table of n, a(n) for n = 1..457</a>

%t 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 *)

%t Select[Accumulate[Range[1500]],FreeQ[IntegerDigits[#],0]&&OddQ[Sqrt[8 Times@@IntegerDigits[ #]+1]]&] (* _Harvey P. Dale_, May 01 2023 *)

%o (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

%Y Cf. A000217, A002473, A007954, A061380.

%K nonn,base

%O 1,2

%A _Amarnath Murthy_, Apr 05 2002

%E More terms from _Jason Earls_ and _Lior Manor_ May 15 2002