This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A239058 #37 Mar 08 2024 11:59:31
%S A239058 1,11,13,17,19,31,41,61,71,101,103,107,109,113,125,127,131,137,139,
%T A239058 149,151,157,163,167,173,179,181,191,193,197,199,211,241,251,271,281,
%U A239058 311,313,317,331,401,419,421,431,461,491,521,541,571,601,613,617,619,631,641,661,691,701,719,751,761,811,821,881,911,919,941,971
%N A239058 Numbers whose divisors all appear as a substring in their decimal expansion.
%C A239058 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).
%C A239058 Are 1 and 125 the only nonprime terms in this sequence?
%C A239058 No: 17692313, 4482669527413081, 21465097175420089, and 567533481816008761 are members. - _Charles R Greathouse IV_, Mar 09 2014
%C A239058 See A239060 for the nonprime terms of this sequence, which include in particular the squares of terms of A115738 (unless such a square would not have a digit 1).
%H A239058 Robert Israel, <a href="/A239058/b239058.txt">Table of n, a(n) for n = 1..10000</a>
%H A239058 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%e A239058 All primes having the digit 1 (A208270) are in this sequence, because {1, p} are the only divisors of a prime p.
%e A239058 The divisors of 125 are {1, 5, 25, 125}; it can be seen that all of them occur as a substring in 125, therefore 125 is in this sequence.
%o A239058 (PARI) is(n,d=vecextract(divisors(n),"^-1"))={ setminus(select(x->x<10,d),Set(digits(n)))&&return;!for(L=2,#Str(d[#d]),setminus(select(x->x
%o A239058 <10^L&&x>=10^(L-1),d),Set(concat(vector(L,o,digits(n\10^(L-o),10^L)))))&&return)}
%o A239058 (PARI) overlap(long,short)=my(D=10^#digits(short)); while(long>=short, if(long%D==short,return(1));long\=10); 0
%o A239058 is(n)=my(d=divisors(n)); forstep(i=#d-1,1,-1, if(!overlap(n,d[i]), return(0))); 1 \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A239058 Cf. A092911, A011531, A121041, A121022-A121040, A018834.
%K A239058 nonn,base
%O A239058 1,2
%A A239058 _M. F. Hasler_, Mar 09 2014