A061380 Triangular numbers with product of digits also a triangular number.

0, 1, 3, 6, 10, 66, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1326, 1540, 1770, 1830, 2016, 2080, 2556, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 5671, 6105

Offset: 1

Author

Amarnath Murthy, May 02 2001

Keywords

• nonn
• base
• easy

Examples

			153 is a triangular number and the product of digits 15 is also a triangular number.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A061867, A069077, A117710.

Programs

Magma

[t: n in [0..110] | IsSquare(8*p+1) where p is &*Intseq(t) where t is (n*(n+1) div 2)];  // Bruno Berselli, Jun 30 2011

Maple

q:= n-> (l-> issqr(1+8*mul(i,i=l)))(convert(n, base, 10)):
select(q, [seq(i*(i+1)/2, i=0..110)])[];  # Alois P. Heinz, Mar 17 2023

Mathematica

tn=Table[n (n+1)/2, {n, 0, 110}] ;Select[tn,MemberQ[tn,Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)

PARI

isok(k) = ispolygonal(k, 3) && ispolygonal(vecprod(digits(k)), 3); \\ Michel Marcus, Mar 17 2023

Extensions

More terms from Erich Friedman, May 08 2001

Offset 1 from Michel Marcus, Mar 17 2023