A068189 -id:A068189 - cp's OEIS frontend

A069716 Smallest number such that the LCM of the digits equals n, or 0 if no such number exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 0, 34, 0, 27, 35, 0, 0, 29, 0, 45, 37, 0, 0, 38, 0, 0, 0, 47, 0, 56, 0, 0, 0, 0, 57, 49, 0, 0, 0, 58, 0, 67, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 345, 0, 0, 79, 0, 0, 0, 0, 0, 0, 257, 0, 89, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 347, 0, 0, 0, 0, 0, 259, 0, 0

Offset: 1

Labos Elemer, Apr 02 2002

If n is a prime with more than one digit, a(n) = 0. - Alonso del Arte, Dec 20 2015

More generally, if prime p >= 11 divides n then a(n) = 0, if 7^2 | n or 5^2 | n or 3^3 | n or 2^4 | n, then a(n) = 0. Consequently, a(n) = 0 for all n > 2520. This arises naturally by noting lcm{1,2,...,9} = 2520. - Sean A. Irvine, May 15 2024

			a(20) = 45 because lcm(4, 5) = 20. If one solution exists, then an infinite number of solutions exist. For n = 20, e.g., 455, 445555555, 545544 etc. are also solutions.

Sean A. Irvine, Table of n, a(n) for n = 1..2520 (includes all nonzero terms)

Cf. A068189, A069716.

digLCMSeek[x_] := Apply[LCM, IntegerDigits[x]]; A069716 = Table[0, {256}]; Do[s = digLCMSeek[n]; If[s < 257 && A069716[[s]] == 0, A069716[[s]] = n], {n, 10000}]; A069716

A085123 Smallest member of A002473 whose digital product = A002473(n), or 0 if no such number exists.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 126, 27, 35, 28, 36, 45, 0, 64

Offset: 1

Amarnath Murthy, Jul 06 2003

Conjecture: No entry is zero.
Next term (A002473(n) = 21) is either 0 or > 10^100. - David Wasserman, Jan 27 2005
a(17) = 0, because A002473(17) = 21 = 3*7 and the last two digits of every member of A002473 greater than 7 contain a digit other than 1, 3, and 7. - Robert Israel, Nov 23 2019
Similarly, a(n) = 0 whenever n >=17 and A002473(n) is coprime to 10. - Robert Israel, Nov 24 2019

			20 is a member of A002473 and the corresponding term is 45 which is also a member of A002473.

Cf. A002473, A068129.

Cf. A068189.

a(17) and a(18) from Robert Israel, Nov 23 2019

cp's OEIS Frontend

A069716 Smallest number such that the LCM of the digits equals n, or 0 if no such number exists.

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