A239060 Nonprime numbers whose divisors all appear as a substring in the number's decimal expansion.

1, 125, 17692313

Offset: 1

Author

M. F. Hasler, Mar 09 2014

Keywords

• nonn
• base
• bref
• more

Comments

This is the subsequence of A239058 without the primes having a digit 1, A208270. It is thus a subsequence of A092911 (all divisors can be formed using the digits of the number) which is a subsequence of A011531 (numbers having the digit 1).

The term a(3)=17692313=A239058(870356), as well as the numbers 4482669527413081, 21465097175420089, and 567533481816008761 which are also members, were found by Charles R Greathouse IV, Mar 09 2014

The square of any term of A115738 is a member of this sequence. The above larger examples are of that form.

a(4) > 10^12. - Giovanni Resta, Sep 08 2018

Examples

			The divisors of 17692313 are {1, 23, 769231, 17692313}; it can be seen that all of them occur as a substring in 17692313, therefore 17692313 is in this sequence.
		

Links

• Giovanni Resta, Terms of the form p*q, with p and q primes, p < 50000, q < 10^100
• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A092911, A011531, A121041, A121022-A121040, A018834.

Programs

PARI

is(n)=!isprime(n)&&is_A239058(n)

PARI

overlap(long,short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short,return(1));long\=10); 0
is(n)=my(d=divisors(n)); #d!=2 && !forstep(i=#d-1,1,-1, if(!overlap(n,d[i]), return(0))) \\ Charles R Greathouse IV, Mar 09 2014