A095048 Number of distinct digits needed to write all positive divisors of n in decimal representation.

1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 1, 5, 2, 4, 3, 5, 2, 6, 2, 5, 4, 2, 3, 6, 3, 4, 5, 5, 3, 6, 2, 6, 2, 5, 4, 7, 3, 5, 3, 6, 2, 6, 3, 3, 5, 5, 3, 6, 4, 4, 4, 6, 3, 9, 2, 7, 5, 5, 3, 7, 2, 4, 6, 6, 4, 4, 3, 7, 5, 7, 2, 8, 3, 5, 5, 8, 2, 7, 3, 7, 6, 4, 3, 7, 4, 6, 6, 4, 3, 9, 4, 6, 3, 5, 3, 7, 3, 6, 3, 5, 2, 8

Offset

1,2

Comments

a(n) <= 10, a(A095050(n)) = 10.

a(A206159(n)) <= 2. - Reinhard Zumkeller, Feb 05 2012

Almost all (in the sense of natural density) terms of this sequence are equal to 10. - Charles R Greathouse IV, Nov 16 2022

Links

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

Example

Set of divisors of n=10: {1,2,5,10}, therefore a(10) = #{0,1,2,5} = 4.
Set of divisors of n=16: {1,2,4,8,16}, therefore a(16)=#{1,2,4,6,8} = 5.

Maple

A095048 := proc(n)
    local digset ;
    digset := {} ;
    for d in numtheory[divisors](n) do
        digset := digset union convert(convert(d, base, 10), set) ;
    end do:
    nops(digset) ;
end proc:
seq(A095048(n), n=1..80) ; # R. J. Mathar, May 13 2022

Prog

(Haskell)
import Data.List (group, sort)
a095048 = length . group . sort . concatMap show . a027750_row
-- Reinhard Zumkeller, Feb 05 2012
(Python)
from sympy import divisors
def a(n):
    s = set("1"+str(n))
    if len(s) == 10: return 10
    for d in divisors(n, generator=True):
        s |= set(str(d))
        if len(s) == 10: return 10
    return len(s)
print([a(n) for n in range(1, 99)]) # Michael S. Branicky, Nov 16 2022
(PARI) a(n) = my(d = divisors(n), s = 0); for(i = 1, #d, v = digits(d[i]); for(j = 1, #v, s = bitor(s, 1<<v[j]); if(s == 1023, return(10)))); hammingweight(s) \\ David A. Corneth, Nov 16 2022

Crossrefs

Cf. A095049, A095050, A043537.

Cf. A027750, A059436.

Sequence in context: A179940 A138707 A358099 * A332268 A355593 A355302

Adjacent sequences: A095045 A095046 A095047 * A095049 A095050 A095051

Keyword

nonn,base

Author

Reinhard Zumkeller, May 28 2004

Status

approved