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A120712 Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.

%I A120712 #30 Oct 01 2024 13:17:09
%S A120712 4,6,9,21,22,25,33,39,46,49,51,54,58,78,82,93,99,111,115,121,133,141,
%T A120712 142,147,153,154,159,162,166,169,174,177,186,187,189,201,205,219,226,
%U A120712 235,237,247,249,253,262,267,274,286,289,291,294,301,318
%N A120712 Numbers k with the property that the concatenation of the nontrivial divisors of k (i.e., excluding 1 and k) is a prime.
%H A120712 T. D. Noe, <a href="/A120712/b120712.txt">Table of n, a(n) for n = 1..1000</a>
%e A120712    k |    divisors    | concatenation
%e A120712   ---+----------------+--------------
%e A120712    4 | (1) 2      (4) |        2
%e A120712    6 | (1) 2, 3   (6) |       23
%e A120712    9 | (1) 3      (9) |        3
%e A120712   21 | (1) 3, 7  (21) |       37
%e A120712   22 | (1) 2, 11 (22) |      211
%e A120712   25 | (1) 5     (25) |        5
%e A120712   33 | (1) 3, 11 (33) |      311
%e A120712   39 | (1) 3, 13 (39) |      313
%p A120712 with(numtheory):
%p A120712 for k from 2 to 1000 do:
%p A120712 v0:=divisors(k):
%p A120712 nn:=nops(v0):
%p A120712 if nn > 2 then
%p A120712 v1:=[seq(v0[j],j=2..nn-1)]:
%p A120712 v2:=cat(seq(convert(v1[n],string),n=1..nops(v1))):
%p A120712 v3:=parse(v2):
%p A120712 if isprime(v3) = true then lprint(k,v3) fi:
%p A120712 fi:
%p A120712 od: # _Simon Plouffe_
%t A120712 fQ[n_] := PrimeQ@ FromDigits@ Most@ Rest@ Divisors@ n; Select[ Range[2, 320], fQ]
%o A120712 (Python)
%o A120712 from sympy import divisors, isprime
%o A120712 def ok(n):
%o A120712     s = "".join(str(d) for d in divisors(n)[1:-1])
%o A120712     return s != "" and isprime(int(s))
%o A120712 print([k for k in range(319) if ok(k)]) # _Michael S. Branicky_, Oct 01 2024
%Y A120712 Cf. A037274, A037278, A037279, A106708, A120713, A120716.
%Y A120712 Cf. A130139, A130140, A130141, A130142.
%K A120712 nonn,base
%O A120712 1,1
%A A120712 _Eric Angelini_, Jul 19 2007
%E A120712 Name edited by _Michel Marcus_, Mar 09 2023