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A161344
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Numbers n with A033676(n)=2, where A033676 is the largest divisor <= sqrt(n).
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46
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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
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OFFSET
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1,1
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COMMENTS
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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. [R. J. Mathar, 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). [Zak Seidov, Jul 18 2009]
Contribution from Omar E. Pol, 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. [Franklin T. Adams-Watters, Aug 06 2009]
See also A163280, the main entry for this sequence. [Omar E. Pol, Oct 24 2009]
Also A100484 UNION 8. - Omar E. Pol, Nov 29 2012 (after Seidov and Hasler).
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LINKS
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Table of n, a(n) for n=1..56.
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
O. E. Pol. Illustration of initial terms of A008578, A161344, A161345, A161424
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FORMULA
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A161344 = 2*A000040 union {8}. - M. F. Hasler, Nov 27 2012
a(n) = 2*A046022(n+1) = 2*A175787(n). - Omar E. Pol, Nov 27 2012
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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; [R. J. Mathar, Jun 24 2009]
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MATHEMATICA
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a[n_] := If[n <= 3, 2n+2, 2*Prime[n-1]]; Table[a[n], {n, 1, 56}] (* Jean-François Alcover, Nov 26 2012, after Zak Seidov *)
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PROG
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(PARI) a(n)=if(n>3, prime(n-1), n+1)*2 \\ - M. F. Hasler, Nov 27 2012
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CROSSREFS
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Cf. A000005, A018253, A160811, A160812, A161205, A161346, A033676, A008578, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532, A163925.
Second column of array in A163280. Also, second row of array in A163990.
Sequence in context: A103800 A022449 A088686 * A127792 A062711 A117347
Adjacent sequences: A161341 A161342 A161343 * 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, Jun 20 2009
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EXTENSIONS
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More terms from R. J. Mathar, Jun 24 2009
Definition added by R. J. Mathar, Jun 28 2009
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STATUS
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approved
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