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A006530
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Gpf(n): greatest prime dividing n; a(1)=1.
(Formerly M0428)
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595
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1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 5, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19, 11, 13, 79, 5, 3, 41, 83, 7, 17, 43
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OFFSET
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1,2
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COMMENTS
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The initial term a(1)=1 is purely conventional: 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 largest prime factor. - Daniel Forgues, Jul 05 2011
Greatest noncomposite number dividing n. - Omar E. Pol, Aug 31 2013
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
Handbook of Number Theory, D. S. Mitrinovic et al., Kluwer, Section IV.1.
H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 210.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000 (extended to 100000 by Daniel Forgues)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
G. Back and M. Caragiu, The greatest prime factor and recurrent sequences, Fib. Q., 48 (2010), 358-362.
OEIS Wiki, Greatest prime factor of n
Eric Weisstein's World of Mathematics, Greatest Prime Factor
Index entries for "core" sequences
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FORMULA
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a(n) = A027748(n, A001221(n)) = A027746(n, A001222(n)); a(n)^A071178(n) = A053585(n). - Reinhard Zumkeller, Aug 27 2011
a(n) = A000040(A061395(n)). - M. F. Hasler, Jan 16 2015
a(n) = n + 1 - Sum_{k=1..n}(floor((k!^n)/n)-floor(((k!^n)-1)/n)). - Anthony Browne, May 11 2016
n/a(n) = A052126(n). - R. J. Mathar, Oct 03 2016
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MAPLE
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with(numtheory, divisors); A006530 := proc(n) local i, t1, t2, t3, t4, t5; t1 := divisors(n); t2 := convert(t1, list); t3 := sort(t2); t4 := nops(t3); t5 := 1; for i from 1 to t4 do if isprime(t3[t4+1-i]) then return t3[t4+1-i]; fi; od; 1; end;
# alternative
A006530 := n->max(1, op(numtheory[factorset](n))); # Peter Luschny, Nov 02 2010
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MATHEMATICA
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Table[ FactorInteger[n][[ -1, 1]], {n, 100}] (* Ray Chandler, Nov 12 2005 and modified by Robert G. Wilson v, Jul 16 2014 *)
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PROG
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(PARI) A006530(n)=if(n>1, vecmax(factor(n)[, 1]), 1) \\ Edited to cover n=1. - M. F. Hasler, Jul 30 2015
(MAGMA) [ #f eq 0 select 1 else f[ #f][1] where f is Factorization(n): n in [1..86] ] // Klaus Brockhaus, Oct 23 2008
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CROSSREFS
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Cf. A020639, A034684, A028233, A034699, A053585. See also A052126, A070087, A070089, A061395, A175723.
Cf. A046670 (partial sums), A104350 (partial products).
Sequence in context: A276440 A162325 A197862 * A102095 A109395 A145254
Adjacent sequences: A006527 A006528 A006529 * A006531 A006532 A006533
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KEYWORD
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nonn,nice,easy,core
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Edited by M. F. Hasler, Jan 16 2015
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STATUS
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approved
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