

A055471


Divisible by the product of its nonzero digits.


9



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 24, 30, 36, 40, 50, 60, 70, 80, 90, 100, 101, 102, 104, 105, 110, 111, 112, 115, 120, 128, 132, 135, 140, 144, 150, 175, 200, 208, 210, 212, 216, 220, 224, 240, 250, 300, 306, 312, 315, 360, 384, 400, 432, 480, 500
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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



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
(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;
(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


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



