A061380 -id:A061380 - cp's OEIS frontend

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

Amarnath Murthy, Apr 05 2002

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

Cf. A000217, A002473, A007954, A061380.

[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

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 *)

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

A117710 Pentagonal numbers for which the product of the digits is also a pentagonal number.

Original entry on oeis.org

0, 1, 5, 51, 70, 210, 330, 590, 715, 1001, 1080, 1162, 1520, 1820, 2035, 2380, 2501, 3015, 3290, 3725, 4030, 4510, 5017, 5370, 6112, 6305, 6501, 6700, 6902, 7107, 7740, 8400, 9087, 9560, 9801, 10045, 10292, 10542, 10795, 11051, 11310, 11572, 12105

Offset: 0

Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006

			715 is in the sequence because it is a pentagonal number and the product of its digits 7*1*5=35 is also a pentagonal number.

Cf. A000326, A061380.

pn=Table[n (3 n - 1)/2, {n, 0, 90}] ;Select[pn,MemberQ[pn,Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)

cp's OEIS Frontend

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

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