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

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

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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

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

Cf. A050278, A171102.

Sequence in context: A344702 A044340 A044721 * A339983 A275996 A235292

Adjacent sequences: A095047 A095048 A095049 * A095051 A095052 A095053

Keyword

nonn,base

Author

Reinhard Zumkeller, May 28 2004

Status

approved