

A176553


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


7



1, 3, 7, 9, 13, 21, 31, 37, 67, 73, 79, 97, 103, 109, 121, 151, 163, 181, 183, 193, 219, 223, 229, 237, 277, 283, 307, 363, 367, 373, 381, 409, 433, 439, 471, 487, 489, 499, 511, 523, 571, 601, 603, 607, 613, 619, 657, 669, 709, 733, 787, 811, 817, 819, 823, 841, 867
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OFFSET

1,2


COMMENTS

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
If m is not in A003136, there is a prime p == 2 (mod 3) such that the exponent of p in the factorization of m is odd, then we have 3  1+p  1+p+p^2+...+p^(2*r1)  sigma(m), sigma = A000203 is the sum of divisors, so the concatenation of the divisors of m is also divisible by 3.  Jianing Song, Aug 22 2022


LINKS



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

(Python)
from sympy import divisors, isprime
def ok(m): return m==1 or isprime(int("".join(str(d) for d in divisors(m))))


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



