A358068 Numbers that share a (decimal) digit with the sum of their proper divisors.

6, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 26, 28, 31, 32, 35, 40, 41, 42, 44, 46, 51, 56, 60, 61, 64, 68, 70, 71, 72, 74, 76, 80, 84, 86, 91, 93, 95, 96, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 120, 121, 124, 125, 126, 127, 128, 130, 131, 132, 135, 136

Offset: 1

Author

Wesley Ivan Hurt, Oct 29 2022

Keywords

• nonn
• base

Examples

			72 is in the sequence since 72 shares a digit with the sum of its proper divisors 123. Both numbers share the digit "2".
		

Links

• Wikipedia, Table of divisors

Crossrefs

Cf. A001065, A357929.

Programs

PARI

isok(n) = #setintersect(Set(digits(sigma(n)-n)), Set(digits(n))); \\ Michel Marcus, Oct 30 2022

Python

from itertools import count, islice
from sympy import divisor_sigma
def A358068_gen(startvalue=2): # generator of terms >= startvalue
    for n in count(max(startvalue,2)):
        s = set(str(divisor_sigma(n)-n))
        if any(d in s for d in set(str(n))):
            yield n
A358068_list = list(islice(A358068_gen(),30)) # Chai Wah Wu, Oct 29 2022