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A079879 Median prime factor: a(1)=1 and for n>1: least prime p such that not more than floor(Omega(n)/2) prime factors are greater than p; Omega(n) is the total number of prime factors of n (A001222). 4
1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, 2, 17, 3, 19, 2, 3, 2, 23, 2, 5, 2, 3, 2, 29, 3, 31, 2, 3, 2, 5, 2, 37, 2, 3, 2, 41, 3, 43, 2, 3, 2, 47, 2, 7, 5, 3, 2, 53, 3, 5, 2, 3, 2, 59, 2, 61, 2, 3, 2, 5, 3, 67, 2, 3, 5, 71, 2, 73, 2, 5, 2, 7, 3, 79, 2, 3, 2, 83, 2, 5, 2, 3, 2, 89, 3, 7, 2, 3, 2, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A020639(n)<= a(n)<=A006530(n);

a(m)=A020639(m)=A006530(m) iff m is a prime power (A000961).

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(30)=a(2*3*5)=3; a(60)=a(2*2*3*5)=2; a(72)=a(2*2*2*3*3)=2; a(90)=a(2*3*3*5)=3; a(108)=a(2*2*3*3*3)=3; a(144)=a(2*2*2*2*3*3)=2; a(216)=a(2*2*2*3*3*3)=2.

MAPLE

f:= proc(n) local F, F2, m, i;

    F:= sort(ifactors(n)[2], (i, j) -> i[1]<j[1]);

    F2:= ListTools:-PartialSums(map2(op, 2, F));

    for i from 1 do

      if 2*F2[i]>=F2[-1] then return F[i][1] fi

    od

end proc:

1, seq(f(n), n=2..100); # Robert Israel, Aug 25 2015

MATHEMATICA

f[n_] := Block[{p = Flatten[Table[#1, {#2}] & @@@ FactorInteger@ n], len}, len = Length@ p; If[OddQ@ len, p[[1 + Floor[len/2]]], p[[len/2]]]]; {1}~Join~Table[f@ n, {n, 2, 96}] (* Michael De Vlieger, Aug 25 2015 *)

CROSSREFS

Cf. A033676, A001222, A079880, A079881.

Sequence in context: A020639 A092067 A214606 * A071889 A091963 A067695

Adjacent sequences:  A079876 A079877 A079878 * A079880 A079881 A079882

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 13 2003

EXTENSIONS

Typo fixed by Franklin T. Adams-Watters, Jul 10 2012

STATUS

approved

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Last modified December 13 17:30 EST 2017. Contains 295959 sequences.