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A095050 Numbers such that all ten digits are needed to write all positive divisors in decimal representation.

%I A095050 #31 Nov 16 2022 13:53:11
%S A095050 108,216,270,304,306,312,324,360,380,406,432,450,504,540,570,608,612,
%T A095050 624,630,648,654,702,708,714,720,728,756,760,780,810,812,864,870,900,
%U A095050 910,912,918,924,936,945,954,972,980,1008,1014,1026,1032,1036,1038
%N A095050 Numbers such that all ten digits are needed to write all positive divisors in decimal representation.
%C A095050 A095048(a(n)) = 10.
%C A095050 Numbers n such that A037278(n), A176558(n) and A243360(n) contain 10 distinct digits. - _Jaroslav Krizek_, Jun 19 2014
%C A095050 Once a number is in the sequence, then all its multiples will be there too. The list of primitive terms begin: 108, 270, 304, 306, 312, 360, 380, ... - _Michel Marcus_, Jun 20 2014
%C A095050 Pandigital numbers A050278 and A171102 are subsequences. - _Michel Marcus_, May 01 2020
%H A095050 Reinhard Zumkeller, <a href="/A095050/b095050.txt">Table of n, a(n) for n = 1..10000</a>
%F A095050 a(n) ~ n. - _Charles R Greathouse IV_, Nov 16 2022
%e A095050 Divisors of 108 are: [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108] where all digits can be found.
%p A095050 q:= n-> is({$0..9}=map(x-> convert(x, base, 10)[], numtheory[divisors](n))):
%p A095050 select(q, [$1..2000])[];  # _Alois P. Heinz_, Oct 28 2021
%t A095050 Select[Range@2000, 1+Union@@IntegerDigits@Divisors@# == Range@10 &] (* _Hans Rudolf Widmer_, Oct 28 2021 *)
%o A095050 (Haskell)
%o A095050 import Data.List (elemIndices)
%o A095050 a095050 n = a095050_list !! (n-1)
%o A095050 a095050_list = map (+ 1) $ elemIndices 10 $ map a095048 [1..]
%o A095050 -- _Reinhard Zumkeller_, Feb 05 2012
%o A095050 (PARI) isok(m)=my(d=divisors(m), v=[1]); for (k=2, #d, v = Set(concat(v, digits(d[k]))); if (#v == 10, return (1));); #v == 10; \\ _Michel Marcus_, May 01 2020
%o A095050 (Python)
%o A095050 from sympy import divisors
%o A095050 def ok(n):
%o A095050     digits_used = set()
%o A095050     for d in divisors(n):
%o A095050         digits_used |= set(str(d))
%o A095050     return len(digits_used) == 10
%o A095050 print([k for k in range(1040) if ok(k)]) # _Michael S. Branicky_, Oct 28 2021
%Y A095050 Cf. A095048, A059436 (subsequence), A206159.
%Y A095050 Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).
%Y A095050 Sequences of numbers n such that the list of divisors of n contains k distinct digits for 1 <= k <= 10: k = 1: A243534; k = 2: A243535; k = 3: A243536; k = 4: A243537; k = 5: A243538; k = 6: A243539; k = 7: A243540; k = 8: A243541; k = 9: A243542; k = 10: A095050. - _Jaroslav Krizek_, Jun 19 2014
%Y A095050 Cf. A050278, A171102.
%K A095050 nonn,base
%O A095050 1,1
%A A095050 _Reinhard Zumkeller_, May 28 2004