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A095050 Numbers such that all ten digits are needed to write all positive divisors in decimal representation. 18
108, 216, 270, 304, 306, 312, 324, 360, 380, 406, 432, 450, 504, 540, 570, 608, 612, 624, 630, 648, 654, 702, 708, 714, 720, 728, 756, 760, 780, 810, 812, 864, 870, 900, 910, 912, 918, 924, 936, 945, 954, 972, 980, 1008, 1014, 1026, 1032, 1036, 1038 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A095048(a(n)) = 10.
Numbers n such that A037278(n), A176558(n) and A243360(n) contain 10 distinct digits. - Jaroslav Krizek, Jun 19 2014
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
Pandigital numbers A050278 and A171102 are subsequences. - Michel Marcus, May 01 2020
LINKS
FORMULA
a(n) ~ n. - Charles R Greathouse IV, Nov 16 2022
EXAMPLE
Divisors of 108 are: [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108] where all digits can be found.
MAPLE
q:= n-> is({$0..9}=map(x-> convert(x, base, 10)[], numtheory[divisors](n))):
select(q, [$1..2000])[]; # Alois P. Heinz, Oct 28 2021
MATHEMATICA
Select[Range@2000, 1+Union@@IntegerDigits@Divisors@# == Range@10 &] (* Hans Rudolf Widmer, Oct 28 2021 *)
PROG
(Haskell)
import Data.List (elemIndices)
a095050 n = a095050_list !! (n-1)
a095050_list = map (+ 1) $ elemIndices 10 $ map a095048 [1..]
-- Reinhard Zumkeller, Feb 05 2012
(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
(Python)
from sympy import divisors
def ok(n):
digits_used = set()
for d in divisors(n):
digits_used |= set(str(d))
return len(digits_used) == 10
print([k for k in range(1040) if ok(k)]) # Michael S. Branicky, Oct 28 2021
CROSSREFS
Cf. A095048, A059436 (subsequence), A206159.
Cf. A243543 (the smallest number m whose list of divisors contains n distinct digits).
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
Sequence in context: A344702 A044340 A044721 * A339983 A275996 A235292
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, May 28 2004
STATUS
approved

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Last modified March 28 16:58 EDT 2024. Contains 371254 sequences. (Running on oeis4.)