A334929 Positive integers k such that there exists a positive integer m consisting of k identical digits and such that m is a multiple of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 18, 21, 22, 24, 27, 36, 42, 44, 45, 54, 63, 66, 72, 78, 81, 84, 88, 108, 111, 126, 132, 135, 156, 162, 168, 189, 198, 205, 216, 222, 234, 242, 243, 252, 264, 294, 312, 324, 333, 342, 378, 396, 404, 405, 444, 462, 465, 468, 484, 486

Offset: 1

Author

Reiner Moewald, May 16 2020

Keywords

• nonn
• base

Comments

For k=3^t, t>=1 you can always find numbers m.

Examples

			12 is a term since 444444444444 = 12*37037037037.
		

Crossrefs

Cf. A014950.

Programs

Mathematica

ok[n_] := AnyTrue[(10^n - 1)/9 Range@9, Mod[#, n] == 0 &]; Select[ Range[486], ok] (* Giovanni Resta, May 24 2020 *)

Python

t = "1"
list = [1]
for i in range(1, 1000):
    t = "1" + t
    m = int(t)
    weiter = 0
    for k in range(1, 10):
        if k * m % (i + 1) == 0:
            weiter = 1
    if weiter == 1:
        list.append(i + 1)
print(list)