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A006530 Gpf(n): greatest prime dividing n; a(1)=1.
(Formerly M0428)
617
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

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).

LINKS

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

FORMULA

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

If A020639(n) = n [when n is 1 or a prime] then a(n) = n, otherwise a(n) = a(A032742(n)). - Antti Karttunen, Mar 12 2017

MAPLE

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

MATHEMATICA

Table[ FactorInteger[n][[ -1, 1]], {n, 100}] (* Ray Chandler, Nov 12 2005 and modified by Robert G. Wilson v, Jul 16 2014 *)

PROG

(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

(Scheme)

;; The following uses macro definec for the memoization (caching) of the results. A naive implementation of A020639 can be found under that entry. It could be also defined with definec to make it faster on the later calls. See http://oeis.org/wiki/Memoization#Scheme

(definec (A006530 n) (let ((spf (A020639 n))) (if (= spf n) spf (A006530 (/ n spf)))))

;; Antti Karttunen, Mar 12 2017

CROSSREFS

Cf. A020639, A034684, A028233, A034699, A053585. See also A032742, 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

KEYWORD

nonn,nice,easy,core

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by M. F. Hasler, Jan 16 2015

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.