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A134333 Numbers n whose number of prime factors (counted with multiplicity) is a prime factor of n.

%I A134333 #14 Aug 02 2022 17:28:48
%S A134333 4,6,10,12,14,18,22,26,27,30,34,38,42,45,46,58,62,63,66,74,75,78,80,
%T A134333 82,86,94,99,102,105,106,114,117,118,120,122,134,138,142,146,147,153,
%U A134333 158,165,166,171,174,178,180,186,194,195,200,202,206,207,214,218,222,226
%N A134333 Numbers n whose number of prime factors (counted with multiplicity) is a prime factor of n.
%H A134333 Hieronymus Fischer, <a href="/A134333/b134333.txt">Table of n, a(n) for n = 1..10000</a>
%F A134333 a(n) << n log n/(log log n)^k for any fixed k. - _Charles R Greathouse IV_, Sep 14 2015
%e A134333 a(1) = 4, since 4 has 2 prime factors and 2 is a prime factor of 4.
%e A134333 a(4) = 12, since 12 = 2*2*3 has 3 prime factors, and 3 is a prime factor of 12.
%e A134333 a(21) = 75, since 75 = 3*3*5 has 3 prime factors. and 3 is a prime factor of 75.
%e A134333 9 = 3*3 is not a term, since the number of prime factors (=2) is not a divisor of 9.
%e A134333 28 = 2*2*7 is not a term, since the number of prime factors (=3) is not a divisor of 28.
%t A134333 fQ[n_] := Module[{d = Total[Transpose[FactorInteger[n]][[2]]]}, PrimeQ[d] && Mod[n, d] == 0]; Select[Range[2, 226], fQ] (* _T. D. Noe_, Apr 05 2013 *)
%o A134333 (PARI) a(n)=my(t=bigomega(n)); n%t==0 && isprime(t) \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A134333 Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134334, A134344, A134376, A063989.
%K A134333 nonn
%O A134333 1,1
%A A134333 _Hieronymus Fischer_, Oct 23 2007
%E A134333 Sequence definition corrected and examples added by _Hieronymus Fischer_, Apr 05 2013