A134333 - OEIS

%I #14 Aug 02 2022 17:28:48

%S 4,6,10,12,14,18,22,26,27,30,34,38,42,45,46,58,62,63,66,74,75,78,80,

%T 82,86,94,99,102,105,106,114,117,118,120,122,134,138,142,146,147,153,

%U 158,165,166,171,174,178,180,186,194,195,200,202,206,207,214,218,222,226

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

%H Hieronymus Fischer, <a href="/A134333/b134333.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) << n log n/(log log n)^k for any fixed k. - _Charles R Greathouse IV_, Sep 14 2015

%e a(1) = 4, since 4 has 2 prime factors and 2 is a prime factor of 4.

%e a(4) = 12, since 12 = 2*2*3 has 3 prime factors, and 3 is a prime factor of 12.

%e a(21) = 75, since 75 = 3*3*5 has 3 prime factors. and 3 is a prime factor of 75.

%e 9 = 3*3 is not a term, since the number of prime factors (=2) is not a divisor of 9.

%e 28 = 2*2*7 is not a term, since the number of prime factors (=3) is not a divisor of 28.

%t 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 (PARI) a(n)=my(t=bigomega(n)); n%t==0 && isprime(t) \\ _Charles R Greathouse IV_, Sep 14 2015

%Y Cf. A000040, A001222, A100118, A046363, A133620, A133621, A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134334, A134344, A134376, A063989.

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Oct 23 2007

%E Sequence definition corrected and examples added by _Hieronymus Fischer_, Apr 05 2013