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Search: id:A161344
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| A161344 |
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Numbers n such that their largest divisor <= sqrt(n) equals 2. |
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+0
47
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| 4, 6, 8, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Define a sieve operation with parameter s that eliminates integers of the form s^2+s*i (i>=0) from the set A000027 of natural numbers. The sequence lists those natural numbers that are eliminated by the sieve s=2 and cannot be eliminated by any sieve s>=3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009]
After a(3)=8 all terms are 2*prime; for n>3 a(n)=2*prime(n-1)=2*A000040(n-1). [From Zak Seidov (zakseidov(AT)yahoo.com), Jul 18 2009]
Contribution from Omar E. Pol (info(AT)polprimos.com), Jul 18 2009: (Start)
A classification of the natural numbers A000027.
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Numbers n such that their largest divisor <= sqrt(n) equals k
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... k .... Sequence ... Comment .............................
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... 1 ..... A008578 ... (1 together with the prime numbers)
... 2 ..... A161344 ... (This sequence)
... 3 ..... A161345
... 4 ..... A161424
... 5 ..... A161835
... 6 ..... A162526
... 7 ..... A162527
... 8 ..... A162528
... 9 ..... A162529
.. 10 ..... A162530
.. 11 ..... A162531
.. 12 ..... A162532
.. And so on.
(End)
The numbers n whose largest divisor <= sqrt(n) is k are exactly those numbers k*m where m is either a prime >= n or one of the numbers in row k of A163925. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 06 2009]
See also A163280, the main entry for this sequence. [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]
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LINKS
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O. E. Pol, Determinacion geometrica de los numeros primos y perfectos
O. E. Pol, Illustration: Divisors and pi(x)
O. E. Pol, Illustration of initial terms [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]
O. E. Pol. Illustration for A008578, A161344, A161345 and A161424 [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]
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FORMULA
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Numbers n such that A033676(n)=2. [From Omar E. Pol (info(AT)polprimos.com), Jul 05 2009].
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MAPLE
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isA := proc(n, s) if n mod s <> 0 then RETURN(false); fi; if n/s-s >= 0 then RETURN(true); else RETURN(false); fi; end: isA161344 := proc(n) for s from 3 to n do if isA(n, s) then RETURN(false); fi; od: isA(n, 2) ; end: for n from 1 to 3000 do if isA161344(n) then printf("%d, ", n) ; fi; od; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009]
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CROSSREFS
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Cf. A000005, A018253, A160811, A160812, A161203, A161204, A161205, A161346.
Cf. A033676, A008578, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532. [From Omar E. Pol (info(AT)polprimos.com), Jul 05 2009]
Cf. A163925. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 06 2009]
Cf. Second column of array in A163280. Also, second row of array in A163990. [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]
Sequence in context: A103800 A022449 A088686 this_sequence A127792 A062711 A117347
Adjacent sequences: A161341 A161342 A161343 this_sequence A161345 A161346 A161347
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KEYWORD
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easy,nonn
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AUTHOR
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Omar E. Pol (info(AT)polprimos.com), Jun 20 2009
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 24 2009
Definition added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 28 2009
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