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A088387 Prime corresponding to largest prime power factor of n, a(1)=1. 9
1, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 2, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 2, 5, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 3, 37, 19, 13, 2, 41, 7, 43, 11, 3, 23, 47, 2, 7, 5, 17, 13, 53, 3, 11, 2, 19, 29, 59, 5, 61, 31, 3, 2, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19, 11, 13, 79, 2, 3, 41, 83, 7, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Most significant prime factor of n: If n = (p_1^e_1)(p_2^e_2)(p_3^e_3)... and max(p_1^e_1,p_2^e_2,...) = p_k^e_k then a(n) = p_k.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

A034699(n) = a(n)^A088388(n).

a(n*a(n)) = a(n). - Sam Alexander, Dec 15 2003

EXAMPLE

a(6) = a(2*3) = 3 because 3^1 > 2^1;

a(36) = a((2^2)(3^2)) = 3 because 3^2 > 2^2;

a(12) = a((2^2)*3) = 2 because 2^2 > 3^1.

MATHEMATICA

f[n_] := Sort[ {#[[1]]^#[[2]], #[[1]]} & /@ FactorInteger@ n][[ -1, 2]]; Array[f, 85] (* Robert G. Wilson v, Nov 05 2007 *)

a[n_] := MaximalBy[FactorInteger[n], Power @@ # &][[1, 1]];

Array[a, 85] (* Jean-Fran├žois Alcover, Jun 27 2019 *)

PROG

(PARI) A088387(n) = if(1==n, 1, my(f=factor(n), p=0); isprimepower(vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2])), &p); (p)); \\ Antti Karttunen, Jul 22 2018

CROSSREFS

Cf. A034699, A088388, A307746, A307641.

Sequence in context: A273289 A346152 A090662 * A197861 A180506 A273283

Adjacent sequences:  A088384 A088385 A088386 * A088388 A088389 A088390

KEYWORD

easy,nonn

AUTHOR

Reinhard Zumkeller, Sep 28 2003

EXTENSIONS

More terms from Ray Chandler, Dec 20 2003

Edited by N. J. A. Sloane at the suggestion of Stefan Steinerberger, Nov 04 2007

STATUS

approved

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Last modified November 27 04:53 EST 2021. Contains 349346 sequences. (Running on oeis4.)