OFFSET
1,2
COMMENTS
If n is the term then 10n also is. - Zak Seidov, Jun 09 2013
De Koninck and Luca showed that the number of terms of this sequence below x is at least x^0.495 but at most x^0.901 for sufficiently large x. - Tomohiro Yamada, Nov 18 2017
This sequence begins with a run of 12 consecutive terms, from 1 to 12. The maximal length of a run of consecutive integer terms is 13. The smallest example of such a run begins with 1111011111000 and ends with 1111011111012 (Diophante link). - Bernard Schott, Apr 26 2019
These numbers are called "nombres prodigieux" on the French site Diophante. - Bernard Schott, Apr 26 2019
LINKS
Marius A. Burtea, Table of n, a(n) for n = 1..11442 (terms 1..1000 from Zak Seidov)
Jean-Marie De Koninck and Florian Luca, Positive integers divisible by the product of their nonzero digits, Port. Math. 64 (2007) 75-85. (This proof for upper bounds contains an error. See the paper below)
Jean-Marie De Koninck and Florian Luca, Corrigendum to "Positive integers divisible by the product of their nonzero digits", Portugaliae Math. 64 (2007), 1: 75-85, Port. Math. 74 (2017), 169-170.
Diophante, A365, les nombres prodigieux, July 2016.
Michael Gohn, Joshua Harrington, Sophia Lebiere, Hani Samamah, Kyla Shappell, and Tony W. H. Wong, Arithmetic Progressions of b-Prodigious Numbers, J. Int. Seq., Vol. 25 (2022), Article 22.8.7.
MATHEMATICA
Select[Range[5000], IntegerQ[ #/(Times @@ Select[IntegerDigits[ # ], # > 0 &])] &] (* Alonso del Arte, Aug 04 2004 *)
PROG
(MATLAB) m=1;
for n=1:1000
v=dec2base(n, 10)-'0';
v = v(v~=0);
if mod(n, prod(v))==0
sol(m)=n;
m=m+1;
end
end
sol % Marius A. Burtea, May 07 2019
(Magma) m:=1; sol:=[];
for n in [1..1000] do
v:=Intseq(n, 10);
while &*v eq 0 do; Exclude(~v, 0); end while;
if n mod &*(v) eq 0 then ; sol[m]:=n; m:=m+1; end if;
end for;
sol // Marius A. Burtea, May 07 2019
(Python)
from math import prod
def ok(n): return n > 0 and n%prod([int(d) for d in str(n) if d!='0']) == 0
print(list(filter(ok, range(501)))) # Michael S. Branicky, Jul 27 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Jul 05 2000
EXTENSIONS
Corrected by Patrick De Geest, Aug 15 2000
STATUS
approved