A209931 Numbers k such that smallest digit of all divisors of k is 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 111

Offset: 1

Author

Jaroslav Krizek, Mar 20 2012

Keywords

• nonn
• base

Comments

Also numbers k such that smallest digit of concatenation of all divisors of k (A037278 or A176558) is 1.

Sequence is not the same as A052382, first deviation is at a(173): A052382(173) = 212, a(173) = 213. [Corrected by Michael S. Branicky, Jul 01 2025.]

Sequence is not the same as A067251, first deviation is at a(91): A067251 (91) = 101, a(91) = 111.

Complement of A209932.

Examples

			Number 24 is in sequence because smallest digit of all divisors of 24 (1, 2, 4, 8, 3, 6, 12, 24) is 1.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052382, A067251, A209929 (smallest digit of all divisors of n).

Programs

Maple

isA209931 := proc(n)
    digsdiv := {} ;
    for d in numtheory[divisors](n) do
        dgs := convert(convert(d,base,10),set) ;
        digsdiv := digsdiv union dgs ;
    end do:
    if 0 in digsdiv then
        false;
    else
        true ;
    end if;
end proc:
A209931 := proc(n)
    option remember;
    if n =1 then
        1;
    else
        for a from procname(n-1)+1 do
            if isA209931(a) then
                return a;
            end if;
        end do;
    end if;
end proc:
seq(A209931(n),n=1..120) ;# R. J. Mathar, Dec 28 2023

Mathematica

Select[Range[100], Min[IntegerDigits[Divisors[#]]] == 1 &] (* Paolo Xausa, Jul 03 2025 *)

Python

from sympy import divisors
def ok(n): return all('0' not in str(d) for d in divisors(n, generator=True))
print([k for k in range(1, 112) if ok(k)]) # Michael S. Branicky, Jul 01 2025