Search: id:A007774
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%I A007774
%S A007774 6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,48,
%T A007774 50,51,52,54,55,56,57,58,62,63,65,68,69,72,74,75,76,77,80,82,85,86,87,
%U A007774 88,91,92,93,94,95,96,98,99,100,104,106,108,111,112,115,116,117,118
%N A007774 Numbers that are divisible by exactly 2 different primes.
%C A007774 Every group of order p^a * q^b is solvable (Burnside, 1904). [From Franz 
               Vrabec (franz.vrabec(AT)aon.at), Sep 14 2008]
%D A007774 W. Burnside, On groups of order p^alpha q^beta, Proc. London Math. Soc. 
               (2) 1 (1904), 388-392. [From Franz Vrabec (franz.vrabec(AT)aon.at), 
               Sep 14 2008]
%H A007774 T. D. Noe, <a href="b007774.txt">Table of n, a(n) for n=1..1000</a>
%F A007774 omega(a(n)) = A001221(a(n)) = 2. - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Sep 20 2005
%e A007774 20 is OK because 20=2^2*5 with two distinct prime divisors 2, 5.
%p A007774 with(numtheory,factorset):f := proc(n) if nops(factorset(n))=2 then RETURN(n) 
               fi; end;
%Y A007774 Cf. A001358 (products of two primes), A014612 (products of three primes), 
               A014613 (products of four primes), A014614 (products of five primes), 
               where the primes are not necessarily distinct.
%Y A007774 See also A074969, A051270, A033993, A033992.
%Y A007774 Cf. A001358, A014612, A014613, A014614, A074969, A051270, A033993, A033992, 
               A000040.
%Y A007774 Cf. A112801.
%Y A007774 Cf. A006881, A046380, A046387, A067885 (product of exactly 2, 4, 5, 6 
               distinct primes respectively).
%Y A007774 Subsequence of A085736. [From Franz Vrabec (franz.vrabec(AT)aon.at), 
               Sep 14 2008]
%Y A007774 Sequence in context: A064040 A024619 A106543 this_sequence A030231 A056760 
               A084227
%Y A007774 Adjacent sequences: A007771 A007772 A007773 this_sequence A007775 A007776 
               A007777
%K A007774 nonn
%O A007774 1,1
%A A007774 ltp1000(AT)hermes.cam.ac.uk

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