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Integers whose number of distinct prime divisors is prime.
4

%I #33 Apr 18 2024 21:46:24

%S 6,10,12,14,15,18,20,21,22,24,26,28,30,33,34,35,36,38,39,40,42,44,45,

%T 46,48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,

%U 78,80,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,102,104,105

%N Integers whose number of distinct prime divisors is prime.

%C For all terms below 210 this sequence and A024619 are identical.

%H Harry J. Smith, <a href="/A064040/b064040.txt">Table of n, a(n) for n = 1..1000</a>

%e 210 = 2*3*5*7 has 4 prime factors, hence it is not here, but it is part of A024619.

%p q:= n-> isprime(nops(ifactors(n)[2])):

%p select(q, [$1..210])[]; # _Alois P. Heinz_, Apr 18 2024

%t Select[Range[200], PrimeQ[PrimeNu[#]] &] (* _Paolo Xausa_, Mar 28 2024 *)

%o (PARI) n=0; for (m=1, 10^9, if (isprime(omega(m)), write("b064040.txt", n++, " ", m); if (n==1000, break))) \\ _Harry J. Smith_, Sep 06 2009

%o (PARI) is(n)=isprime(omega(n)) \\ _Charles R Greathouse IV_, Sep 18 2015

%Y Cf. A001221, A024619, A000977, A033992, A007774, A033993, A051270, A063989.

%K nonn,easy

%O 1,1

%A _Lior Manor_, Aug 23 2001

%E Edited by _Charles R Greathouse IV_, Mar 18 2010

%E Name edited by _Michel Marcus_, Oct 16 2023