A068190 Largest number whose digit product equals n; a(n)=0 if no such number exists, e.g., when n has a prime factor larger than 7; no digit=1 is permitted to avoid an infinite number of solutions.

0, 2, 3, 22, 5, 32, 7, 222, 33, 52, 0, 322, 0, 72, 53, 2222, 0, 332, 0, 522, 73, 0, 0, 3222, 55, 0, 333, 722, 0, 532, 0, 22222, 0, 0, 75, 3322, 0, 0, 0, 5222, 0, 732, 0, 0, 533, 0, 0, 32222, 77, 552, 0, 0, 0, 3332, 0, 7222, 0, 0, 0, 5322, 0, 0, 733, 222222, 0, 0, 0, 0, 0

Offset

1,2

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

If a solution exists, a(n) is the concatenation of prime factors with repetitions and in order of magnitude, otherwise a(n)=0.

Mathematica

Array[If[#[[-1, 1]] > 7, 0, FromDigits@ Reverse@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, #]] &@ FactorInteger@ # &, 69] /. 1 -> 0 (* Michael De Vlieger, Dec 08 2018 *)

Prog

(PARI) a(n) = {my(res = []); for(i=2, 9, v = valuation(n, i); if(v > 0, res = concat(vector(v, j, i), res); n/=i^v)); if(n==1, fromdigits(res), 0)} \\ David A. Corneth, Jul 31 2017

Crossrefs

Cf. A001222, A002473, A007954, A067734, A068183-A068187, A068189-A068191.

Sequence in context: A073647 A073646 A037276 * A084796 A084797 A163902

Adjacent sequences: A068187 A068188 A068189 * A068191 A068192 A068193

Keyword

base,nonn

Author

Labos Elemer, Feb 19 2002

Extensions

a(36) corrected by David A. Corneth, Jul 31 2017

Status

approved