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

Author

Reinhard Zumkeller, May 28 2004

Keywords

• nonn
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A095049, A095050, A043537.

Cf. A027750, A059436.

Programs

Haskell

import Data.List (group, sort)
a095048 = length . group . sort . concatMap show . a027750_row
-- Reinhard Zumkeller, Feb 05 2012

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

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<David A. Corneth, Nov 16 2022

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