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A307792
Triangular numbers t(n) such that n / (product of decimal digits of t(n)) is an integer.
1
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
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
KEYWORD
base,nonn,more
AUTHOR
Ctibor O. Zizka, Apr 29 2019
STATUS
approved