A307792 Triangular numbers t(n) such that n / (product of decimal digits of t(n)) is an integer.

1, 15, 21, 11325, 41616, 71631

Offset

1,2

Comments

The name implies that t(n) must be zeroless. I conjecture 1 and 15 are the only two terms with the property n = product of decimal digits of t(n). Are all terms bigger than 1 divisible by 3?

The next term, if it exists, is > 5*10^17. - Vaclav Kotesovec, Apr 30 2019

The next term, if it exists, is > 3.2*10^24. - Giovanni Resta, May 02 2019

Links

Table of n, a(n) for n=1..6.

Example

For n = 150, t(150) = 11325, product of decimal digits of t(150) = 30, n / product of decimal digits of t(n) = 150 / 30 = 5 so t(150) = 11325 is in the sequence;
for n = 378, t(378) = 71631, product of decimal digits of t(378) = 126, n / product of decimal digits of t(n) = 378 / 126 = 3 so t(378) = 71631 is in the sequence.

Mathematica

idx = Quiet[Select[Range[100000], Divisible[#, Product[j, {j, IntegerDigits[#*(# + 1)/2]}]] &]]; idx*(idx + 1)/2 (* Vaclav Kotesovec, Apr 30 2019 *)

Crossrefs

Cf. A000217, A007954, A052382.

Sequence in context: A265153 A219214 A205597 * A236764 A300958 A066758

Adjacent sequences: A307789 A307790 A307791 * A307793 A307794 A307795

Keyword

base,nonn,more

Author

Ctibor O. Zizka, Apr 29 2019

Status

approved