A085124 Smallest multiple of n whose digital product is also a positive multiple of n, or 0 if no such number exists.

1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 0, 168, 0, 378, 135, 48, 0, 36, 0, 0, 273, 0, 0, 168, 525, 0, 999, 476, 0, 0, 0, 288, 0, 0, 175, 1296, 0, 0, 0, 0, 0, 378, 0, 0, 495, 0, 0, 384, 3577, 0, 0, 0, 0, 1296, 0, 728, 0, 0, 0, 0, 0, 0, 1197, 448, 0, 0, 0, 0, 0, 0, 0, 1368, 0, 0, 3525, 0, 0, 0, 0, 0

Offset

1,2

Comments

a(n) = 0 if n is not a term of A002473 (i.e., not a 7-smooth number).

a(n) = 0 if n is a multiple of 10.

Conjecture: otherwise, a(n) is positive.

Sequence may be redefined to avoid large number of zeros by restricting it to members of A002473 which are not divisible by 10.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) local k, v;
   if n mod 10 = 0 or max(NumberTheory:-PrimeFactors(n))>7 then return 0 fi;
   for k from n by n do
     v:= convert(convert(k, base, 10), `*`);
     if v > 0 and v mod n = 0 then return k fi
   od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 28 2025

Crossrefs

Cf. A002473, A073909.

Sequence in context: A093691 A379512 A004176 * A252648 A054054 A115353

Adjacent sequences: A085121 A085122 A085123 * A085125 A085126 A085127

Keyword

base,nonn

Author

Amarnath Murthy, Jul 06 2003

Extensions

More terms from David Wasserman, Jan 27 2005

Comments edited by Jon E. Schoenfield, Mar 30 2014

Definition clarified by Robert Israel, Dec 28 2025

Status

approved