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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) 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 Superset of A007602. Cf. A007088. Sequence in context: A246088 A071204 A002796 * A278328 A066254 A167904 Adjacent sequences: A055468 A055469 A055470 * A055472 A055473 A055474 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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