A069716 - OEIS

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

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OFFSET

1,2

COMMENTS

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

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A068189, A069716.

Sequence in context: A349279 A347189 A068189 * A095289 A174141 A343403

Adjacent sequences: A069713 A069714 A069715 * A069717 A069718 A069719

KEYWORD

easy,nonn,base

AUTHOR

Labos Elemer, Apr 02 2002

STATUS

approved