A084227 - OEIS

%I #13 Aug 22 2021 23:54:10

%S 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,38,39,40,44,45,46,48,50,

%T 51,52,54,55,56,57,58,62,63,65,68,69,74,75,76,77,80,82,85,86,87,88,91,

%U 92,93,94,95,96,98,99,104,106,111,112,115,116,117,118,119,122,123,124,129

%N Numbers of the form p*q^k with distinct primes p and q, k>0.

%C A001221(a(n)) = 2 AND A001222(a(n)) = A051903(a(n)) + 1. [Clarified by _N. J. A. Sloane_, Aug 22 2021]

%C See A007774 for the numbers with omega(n) = A001221(n) = 2. - _N. J. A. Sloane_, Aug 22 2021

%H G. C. Greubel, <a href="/A084227/b084227.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) ~ n log n/log log n. - _Charles R Greathouse IV_, Oct 19 2015

%e 80 = 5*2^4, therefore 80 is a term.

%t doit[{p_,q_}]:=Table[{p q^k,q p^k},{k,10}]; Take[Union[Flatten[ doit/@ Subsets[Prime[Range[20]],{2}]]],70] (* _Harvey P. Dale_, May 09 2012 *)

%o (PARI) is(n)=my(f=factor(n)[,2]); #f==2 && vecmin(f)==1 \\ _Charles R Greathouse IV_, Oct 19 2015

%Y Cf. A000961, A006881, A007774.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 20 2003