A079880 a(n) = n/mpf(n), where mpf(n) is the median prime factor of n (A079879).

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 6, 1, 10, 7, 11, 1, 12, 5, 13, 9, 14, 1, 10, 1, 16, 11, 17, 7, 18, 1, 19, 13, 20, 1, 14, 1, 22, 15, 23, 1, 24, 7, 10, 17, 26, 1, 18, 11, 28, 19, 29, 1, 30, 1, 31, 21, 32, 13, 22, 1, 34, 23, 14, 1, 36, 1, 37, 15, 38, 11, 26, 1, 40, 27, 41, 1, 42

Offset

1,4

Comments

A052126(n)<=a(n)<=A032742(n);

a(m)=A032742(m)=A052126(m) iff m is a prime power (A000961).

Links

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

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 n/F[i][1] fi
    od
end proc:
1, seq(f(n), n=2..100); # Robert Israel, Jan 26 2018

Mathematica

mpf[n_] := Module[{fi = FactorInteger[n], ff, Om}, ff = Flatten[Table[ Table[f[[1]], {f[[2]]}], {f, fi}]]; Om = Length[ff]; If[OddQ[Om], ff[[Floor[Om/2]+1]], ff[[Om/2]]]];
a[n_] := n/mpf[n];
Array[a, 100] (* Jean-François Alcover, Mar 09 2019 *)

Crossrefs

a(n)=n/A079879(n), A033676.

Sequence in context: A079554 A247892 A366649 * A366291 A353271 A326139

Adjacent sequences: A079877 A079878 A079879 * A079881 A079882 A079883

Keyword

nonn,look

Author

Reinhard Zumkeller, Jan 13 2003

Status

approved