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A007774
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Numbers that are divisible by exactly 2 different primes.
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27
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| Every group of order p^a * q^b is solvable (Burnside, 1904). [From Franz Vrabec (franz.vrabec(AT)aon.at), Sep 14 2008]
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REFERENCES
| 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]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| omega(a(n)) = A001221(a(n)) = 2. - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 20 2005
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EXAMPLE
| 20 is OK because 20=2^2*5 with two distinct prime divisors 2, 5.
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MAPLE
| with(numtheory, factorset):f := proc(n) if nops(factorset(n))=2 then RETURN(n) fi; end;
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MATHEMATICA
| Select[Range[0, 6! ], Length[FactorInteger[ # ]]==2&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 22 2010]
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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, A046380, A046387, A067885 (product of exactly 2, 4, 5, 6 distinct primes respectively).
Subsequence of A085736. [From Franz Vrabec (franz.vrabec(AT)aon.at), Sep 14 2008]
Sequence in context: A168638 A024619 A106543 * A030231 A056760 A084227
Adjacent sequences: A007771 A007772 A007773 * A007775 A007776 A007777
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KEYWORD
| nonn
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AUTHOR
| ltp1000(AT)hermes.cam.ac.uk
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