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Numbers that share at least 1 (decimal) digit with their largest proper divisor.
1

%I #12 Mar 10 2023 14:46:22

%S 11,13,15,17,19,20,24,25,31,39,40,41,42,45,48,50,51,52,60,61,71,74,75,

%T 80,84,91,93,94,95,98,100,101,102,103,105,107,109,113,119,120,121,122,

%U 123,124,125,126,127,131,133,135,136,137,139,140,141,142,143,147,148,149,150

%N Numbers that share at least 1 (decimal) digit with their largest proper divisor.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Table_of_divisors">Table of divisors</a>

%e 52 is in the sequence since it shares at least one digit with 26, its largest proper divisor. Both numbers share the digit 2.

%t Select[Range[2, 150], Length[Intersection[IntegerDigits[#], IntegerDigits[#/FactorInteger[ #][[1, 1]]]]] > 0 &] (* _Amiram Eldar_, Oct 30 2022 *)

%o (PARI) isok(m) = (m>1) && #setintersect(Set(digits(m)), Set(digits(m/factor(m)[1, 1]))); \\ _Michel Marcus_, Oct 30 2022

%Y Cf. A032742, A357929.

%K nonn,base

%O 1,1

%A _Wesley Ivan Hurt_, Oct 29 2022