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 A034699 Largest prime power factor of n. 45

%I

%S 1,2,3,4,5,3,7,8,9,5,11,4,13,7,5,16,17,9,19,5,7,11,23,8,25,13,27,7,29,

%T 5,31,32,11,17,7,9,37,19,13,8,41,7,43,11,9,23,47,16,49,25,17,13,53,27,

%U 11,8,19,29,59,5,61,31,9,64,13,11,67,17,23,7,71,9,73,37,25,19,11,13,79

%N Largest prime power factor of n.

%C n divides lcm(1, 2, ..., a(n)).

%C a(n) = A210208(n,A073093(n)) = largest term of n-th row in A210208. - _Reinhard Zumkeller_, Mar 18 2012

%C a(n) = smallest m > 0 such that n divides A003418(m). - _Thomas Ordowski_, Nov 15 2013

%C a(n) = n when n is a prime power (A000961). - _Michel Marcus_, Dec 03 2013

%H Antti Karttunen, <a href="/A034699/b034699.txt">Table of n, a(n) for n = 1..65537</a> (first 1000 terms from T. D. Noe)

%F If n = p_1^e_1 *...* p_k^e_k, p_1 < ... < p_k primes, then a(n) = max { p_i^e_i }.

%F a(n) = A088387(n)^A088388(n). - _Antti Karttunen_, Jul 22 2018

%F a(n) = n/A284600(n) = n - A081805(n) = A034684(n) + A100574(n). - _Antti Karttunen_, Aug 06 2018

%t f[n_] := If[n == 1, 1, Max[ #[[1]]^#[[2]] & /@ FactorInteger@n]]; Array[f, 79] (* _Robert G. Wilson v_ Sep 02 2006 *)

%t Array[Max[Power @@@ FactorInteger@ #] &, 79] (* _Michael De Vlieger_, Jul 26 2018 *)

%o a034699 = last . a210208_row

%o -- _Reinhard Zumkeller_, Mar 18 2012, Feb 14 2012

%o (PARI) a(n) = if(1==n,n,my(f=factor(n)); vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2]))); \\ _Charles R Greathouse IV_, Nov 20 2012, check for a(1) added by _Antti Karttunen_, Aug 06 2018

%o (PARI) A034699(n) = if(1==n,n,fordiv(n, d, if(isprimepower(n/d), return(n/d)))); \\ _Antti Karttunen_, Aug 06 2018

%Y Cf. A006530, A010055, A020639, A027750, A034684, A028233, A051283, A052128, A053585, A057110, A060818, A038610, A081805, A088387, A088388, A100574, A210208, A284600.

%K nonn,easy,nice

%O 1,2

%A _David W. Wilson_

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Last modified January 15 18:58 EST 2019. Contains 319170 sequences. (Running on oeis4.)