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A033676
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Largest divisor of n <= sqrt(n).
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47
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1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 4, 1, 3, 1, 4, 3, 2, 1, 4, 5, 2, 3, 4, 1, 5, 1, 4, 3, 2, 5, 6, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 6, 7, 5, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 8, 1, 2, 5, 4, 7, 6, 1, 8, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Contribution from Omar E. Pol (info(AT)polprimos.com), Jul 05 2009: (Start)
Values ... Sequence
.. 1 ..... A008578 (1 together with the prime numbers)
.. 2 ..... A161344
.. 3 ..... A161345
.. 4 ..... A161424
.. 5 ..... A161835
.. 6 ..... A162526
.. 7 ..... A162527
.. 8 ..... A162528
.. 9 ..... A162529
. 10 ..... A162530
. 11 ..... A162531
. 12 ..... A162532
(End)
a(n) = sqrt(n) is a new record iff n is a square. [From Zak Seidov (zakseidov(AT)yahoo.com), Jul 17 2009]
a(n)=A060775(n) unless n is a square, then a(n)=A033677(n)=sqrt(n) is strictly larger than A060775(n). It would be nice to have an efficient algorithm to calculate these functions for n having a large number of divisors, as they occur e.g. in A060776, A060777 and related problems like A182987. - M. F. Hasler, Sep 20 2011.
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REFERENCES
| G. Tenenbaum, pp. 268ff of R. L. Graham et al., eds., Mathematics of Paul Erdos I.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
O. E. Pol, Illustration: Divisors and pi(x) [From Omar E. Pol (info(AT)polprimos.com), Jul 05 2009]
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MAPLE
| A033676 := proc(n) local a, d; a := 0 ; for d in numtheory[divisors](n) do if d^2 <= n then a := max(a, d) ; fi; od: a; end: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 09 2009]
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MATHEMATICA
| LargestDivisor[n_Integer] := Module[{dvs = Divisors[n]}, dvs[[Ceiling[Length@dvs/2]]]]; LargestDivisor /@ Range[100] [From Borislav Stanimirov (prizrak6(AT)yahoo.com), Mar 28 2010]
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PROG
| (PARI) A033676(n) = {local(d); if(n<2, 1, d=divisors(n); d[(length(d)+1)\2])} [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Jan 30 2010]
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CROSSREFS
| A033677(n) * a(n) = n
Cf. A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532. [From Omar E. Pol (info(AT)polprimos.com), Jul 05 2009]
Sequence in context: A072203 A124044 A059981 * A095165 A046805 A034880
Adjacent sequences: A033673 A033674 A033675 * A033677 A033678 A033679
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Typos in A-numbers corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 13 2009
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