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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 (list; graph; refs; listen; history; text; internal format)
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)
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
Superset of A007602.
Cf. A007088.
Sequence in context: A246088 A071204 A002796 * A278328 A066254 A167904
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Jul 05 2000
EXTENSIONS
Corrected by Patrick De Geest, Aug 15 2000
STATUS
approved

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Last modified May 22 21:38 EDT 2024. Contains 372758 sequences. (Running on oeis4.)