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A046411 Composite numbers the concatenation of whose prime factors is a prime.

%I A046411 #28 Jun 12 2021 09:07:19
%S A046411 6,12,18,21,22,28,33,39,46,51,52,54,58,63,66,70,82,84,93,98,111,115,
%T A046411 117,133,141,142,148,154,159,162,165,166,171,172,175,177,182,187,198,
%U A046411 201,205,207,210,219,220,226,232,235,237,245,246,247,249,253,255,261
%N A046411 Composite numbers the concatenation of whose prime factors is a prime.
%C A046411 For the corresponding primes, see A038514. - _Lekraj Beedassy_, Jun 05 2009
%H A046411 Charles R Greathouse IV, <a href="/A046411/b046411.txt">Table of n, a(n) for n = 1..10000</a>
%H A046411 Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>
%e A046411 162 = 2 * 3 * 3 * 3 * 3 and 23333 is a prime, so 162 is in the sequence.
%t A046411 co[n_,k_]:=Nest[FromDigits[Flatten[IntegerDigits[{#,n}]]]&,n,k-1]; Select[Range[261],!PrimeQ[#]&&PrimeQ[FromDigits[Flatten[IntegerDigits[co@@@FactorInteger[#]]]]]&](* _Jayanta Basu_, Jun 04 2013 *)
%o A046411 (PARI) is(n)=my(f=factor(n),s="");for(i=1,#f~,for(j=1,f[i,2],s=Str(s,f[i,1]))); isprime(eval(s)) && !isprime(n) \\ _Charles R Greathouse IV_, May 14 2015
%o A046411 (Python)
%o A046411 from sympy import isprime, factorint
%o A046411 def ok(n):
%o A046411     f = factorint(n)
%o A046411     if sum(e for e in f.values()) < 2: return False
%o A046411     return isprime(int("".join(str(p)*e for p, e in f.items())))
%o A046411 print(list(filter(ok, range(2, 262)))) # _Michael S. Branicky_, Jun 12 2021
%Y A046411 Cf. A037271-A037281.
%Y A046411 Cf. A038514 (corresponding primes), A221220 (factors without multiplicity).
%K A046411 nonn,base
%O A046411 1,1
%A A046411 _Patrick De Geest_, Jun 15 1998
%E A046411 Edited by _Charles R Greathouse IV_, Apr 23 2010
%E A046411 Title clarified by _Sean A. Irvine_, Jan 16 2021