A120712 - OEIS

%I #30 Oct 01 2024 13:17:09

%S 4,6,9,21,22,25,33,39,46,49,51,54,58,78,82,93,99,111,115,121,133,141,

%T 142,147,153,154,159,162,166,169,174,177,186,187,189,201,205,219,226,

%U 235,237,247,249,253,262,267,274,286,289,291,294,301,318

%N Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.

%H T. D. Noe, <a href="/A120712/b120712.txt">Table of n, a(n) for n = 1..1000</a>

%e    k |    divisors    | concatenation

%e   ---+----------------+--------------

%e    4 | (1) 2      (4) |        2

%e    6 | (1) 2, 3   (6) |       23

%e    9 | (1) 3      (9) |        3

%e   21 | (1) 3, 7  (21) |       37

%e   22 | (1) 2, 11 (22) |      211

%e   25 | (1) 5     (25) |        5

%e   33 | (1) 3, 11 (33) |      311

%e   39 | (1) 3, 13 (39) |      313

%p with(numtheory):

%p for k from 2 to 1000 do:

%p v0:=divisors(k):

%p nn:=nops(v0):

%p if nn > 2 then

%p v1:=[seq(v0[j],j=2..nn-1)]:

%p v2:=cat(seq(convert(v1[n],string),n=1..nops(v1))):

%p v3:=parse(v2):

%p if isprime(v3) = true then lprint(k,v3) fi:

%p fi:

%p od: # _Simon Plouffe_

%t fQ[n_] := PrimeQ@ FromDigits@ Most@ Rest@ Divisors@ n; Select[ Range[2, 320], fQ]

%o (Python)

%o from sympy import divisors, isprime

%o def ok(n):

%o     s = "".join(str(d) for d in divisors(n)[1:-1])

%o     return s != "" and isprime(int(s))

%o print([k for k in range(319) if ok(k)]) # _Michael S. Branicky_, Oct 01 2024

%Y Cf. A037274, A037278, A037279, A106708, A120713, A120716.

%Y Cf. A130139, A130140, A130141, A130142.

%K nonn,base

%O 1,1

%A _Eric Angelini_, Jul 19 2007

%E Name edited by _Michel Marcus_, Mar 09 2023