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 A007774 Numbers that are divisible by exactly 2 different primes. 51
 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104, 106, 108, 111, 112, 115, 116, 117, 118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every group of order p^a * q^b is solvable (Burnside, 1904). - Franz Vrabec, Sep 14 2008 Characteristic function for a(n): floor(omega(n)/2) * floor(2/omega(n)) where omega(n) is the number of distinct prime factors of n. - Wesley Ivan Hurt, Jan 10 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 W. Burnside, On groups of order p^alpha q^beta, Proc. London Math. Soc. (2) 1 (1904), 388-392. FORMULA omega(a(n)) = A001221(a(n)) = 2. - Jonathan Vos Post, Sep 20 2005 EXAMPLE 20 is a term because 20 = 2^2*5 with two distinct prime divisors 2, 5. MAPLE with(numtheory, factorset):f := proc(n) if nops(factorset(n))=2 then RETURN(n) fi; end; MATHEMATICA Select[Range[0, 6! ], Length[FactorInteger[ # ]]==2&] (* Vladimir Joseph Stephan Orlovsky, Apr 22 2010 *) Select[Range[120], PrimeNu[#]==2&] (* Harvey P. Dale, Jun 03 2020 *) PROG (Haskell) a007774 n = a007774_list !! (n-1) a007774_list = filter ((== 2) . a001221) [1..] -- Reinhard Zumkeller, Aug 02 2012 (PARI) is(n)=omega(n)==2 \\ Charles R Greathouse IV, Apr 01 2013 CROSSREFS 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. See also A074969, A051270, A033993, A033992. Cf. A001358, A014612, A014613, A014614, A074969, A051270, A033993, A033992, A000040. Cf. A112801. Cf. A006881, A046386, A046387, A067885 (product of exactly 2, 4, 5, 6 distinct primes respectively). Subsequence of A085736. - Franz Vrabec, Sep 14 2008 Cf. A256617 (subsequence). Sequence in context: A106543 A324455 A327476 * A030231 A267114 A275665 Adjacent sequences:  A007771 A007772 A007773 * A007775 A007776 A007777 KEYWORD nonn AUTHOR Luke Pebody (ltp1000(AT)hermes.cam.ac.uk) STATUS approved

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Last modified May 18 04:22 EDT 2021. Contains 343994 sequences. (Running on oeis4.)