

A176553


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


6



1, 3, 7, 9, 13, 21, 31, 37, 67, 73, 79, 97, 103, 109, 121, 151, 163, 181, 183, 193, 219, 223, 229, 237, 27, 283, 307, 363, 367, 373, 381, 409, 433, 439, 471, 487, 489, 499, 511, 523, 571, 601, 603, 607, 63, 619, 657, 669, 709, 733, 787, 811, 817, 819, 823, 841, 867
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OFFSET

1,2


COMMENTS

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


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

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


MATHEMATICA

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


PROG

(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
(PARI) is(n)=my(d=divisors(n)); d[1]="1"; isprime(eval(concat(d)))  n==1 \\ Charles R Greathouse IV, Sep 23 2016


CROSSREFS

Subsequence of A045572.
Sequence in context: A111250 A118643 A043772 * A109370 A018663 A110575
Adjacent sequences: A176550 A176551 A176552 * A176554 A176555 A176556


KEYWORD

nonn,base


AUTHOR

Jaroslav Krizek, Apr 20 2010


EXTENSIONS

Edited and extended by Charles R Greathouse IV, Apr 30 2010


STATUS

approved



