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A020639
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Lpf(n): least prime dividing n (with a(1)=1).
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302
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1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 2, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 2, 43, 2, 3, 2, 47, 2, 7, 2, 3, 2, 53, 2, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 71, 2, 73, 2, 3, 2, 7, 2, 79, 2, 3, 2, 83, 2, 5, 2, 3, 2, 89, 2, 7, 2, 3, 2, 5, 2, 97
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(1) = 1, a(2) = (2*1)/1 = 2; a(n+1) = a(n)*(the smallest prime divisor of (n+1) divided by the largest prime divisor of a(n)). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 28 2004
a(n) = the maximum number of integers such that all pairwise differences are coprime to n. - Max Alekseyev, Mar 17 2006
The unit 1 is not a prime number (although it has been considered so in the past.) 1 is the empty product of prime numbers, thus 1 has no least prime factor. - Daniel Forgues, Jul 05 2011
a(n) = A027746(n,1) = A027748(n,1). [Reinhard Zumkeller, Aug 27 2011]
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REFERENCES
| D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section IV.1.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000 (extended to 100000 by Daniel Forgues)
OEIS Wiki, Least prime factor of n
Eric Weisstein's World of Mathematics, Least Prime Factor
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FORMULA
| A014673(n) = a(A032742(n)); A117357(n) = a(A054576(n)). - Reinhard Zumkeller, Mar 10 2006
A028233(n) = a(n)^A067029(n). - Reinhard Zumkeller, May 13 2006
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MAPLE
| A020639 := proc(n) if n = 1 then 1; else min(op(numtheory[factorset](n))) ; end if; end proc: seq(A020639(n), n=1..20) ; [From R. J. Mathar, Oct 25 2010]
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MATHEMATICA
| f[n_]:=FactorInteger[n][[1, 1]]; Array[f, 120] (* From Robert G. Wilson, Apr 06 2011 *)
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PROG
| (PARI) g(n) = for(x=2, n, a=Vec(factor(x)); print1(a[1][1]", ")) - Cino Hilliard (pseudo.t(AT)comcast.net), Dec 08 2006
(Haskell)
a020639 n = spf a000040_list where
spf (p:ps) | n < p^2 = n
| mod n p == 0 = p
| otherwise = spf ps
-- Reinhard Zumkeller, Jul 13 2011
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CROSSREFS
| Cf. A090368 (bisection).
Cf. A009190, A006530, A034684, A028233, A034699, A053585. See also A046669, A032742, A068319, A088377.
Sequence in context: A135679 A092028 * A092067 A079879 A071889 A091963
Adjacent sequences: A020636 A020637 A020638 * A020640 A020641 A020642
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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