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 A176553 Numbers m such that concatenations of divisors of m are noncomposites. 6

%I

%S 1,3,7,9,13,21,31,37,67,73,79,97,103,109,121,151,163,181,183,193,219,

%T 223,229,237,27,283,307,363,367,373,381,409,433,439,471,487,489,499,

%U 511,523,571,601,603,607,63,619,657,669,709,733,787,811,817,819,823,841,867

%N Numbers m such that concatenations of divisors of m are noncomposites.

%C See A037278(n) = concatenation of divisors of n. See A176555 for corresponding values of concatenations. Complement of A176554 (n) for n >= 2.

%C Do all primes p > 5 have a multiple in this sequence? This holds at least for p < 10^4. - _Charles R Greathouse IV_, Sep 23 2016

%e a(6) = 21: the divisors of 21 are 1,3,7,21, and their concatenation 13721 is noncomposite.

%t Select[Range[10^3], ! CompositeQ@ FromDigits@ Flatten@ IntegerDigits@ Divisors@ # &] (* _Michael De Vlieger_, Sep 23 2016 *)

%o (PARI) genit(iend)=i5=3; print1("1,"); while(i5<=iend,n=i5; while(n%5==0,n+=2); i5=n;f=divisors(n); L1=0; for(h4=1,length(f),L1=L1+length(Str(f[h4]))); myExp=L1; q=0; for(i=1,length(f),adj=length(Str(f[i])); myExp-=adj;q=q+f[i]*10^myExp); if(isprime(q),print1(n,",")); i5+=2); \\ _Bill McEachen_, Sep 22 2016

%o (PARI) is(n)=my(d=divisors(n)); d="1"; isprime(eval(concat(d))) || n==1 \\ _Charles R Greathouse IV_, Sep 23 2016

%Y Subsequence of A045572.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Apr 20 2010

%E Edited and extended by _Charles R Greathouse IV_, Apr 30 2010

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Last modified January 26 10:36 EST 2021. Contains 340438 sequences. (Running on oeis4.)