A079880 - OEIS

%I #13 Mar 09 2019 11:26:11

%S 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,

%T 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,

%U 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

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

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

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

%H Robert Israel, <a href="/A079880/b079880.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%p     for i from 1 do

%p       if 2*F2[i]>=F2[-1] then return n/F[i][1] fi

%p     od

%p end proc:

%p 1, seq(f(n),n=2..100); # _Robert Israel_, Jan 26 2018

%t 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]]]];

%t a[n_] := n/mpf[n];

%t Array[a, 100] (* _Jean-François Alcover_, Mar 09 2019 *)

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

%K nonn,look

%O 1,4

%A _Reinhard Zumkeller_, Jan 13 2003