A175264 - OEIS

%I #12 Mar 11 2014 01:32:51

%S 2,3,2,5,7,2,3,11,13,2,17,19,23,5,3,29,3,31,2,37,41,3,43,47,7,53,59,3,

%T 61,2,3,67,5,71,73,3,79,3,83,3,89,3,97,101,3,103,5,107,109,5,113,3,3,

%U 11,5,3,127,2,5,131,3,137,3,139,5,149,3,151,7,3,157,163,5,167,3,13,5,173,3

%N a(n) = the middle prime among the distinct primes dividing {the n-th positive integer divisible by exactly an odd number of distinct primes}.

%H Harvey P. Dale, <a href="/A175264/b175264.txt">Table of n, a(n) for n = 1..1000</a>

%e The 28th positive integer divisible by exactly an odd number of distinct primes is 60. 60 is factored as 2^2*3*5. The distinct primes dividing 60 are therefore 2, 3, and 5. Since the middle of these primes is 3, then a(28) = 3.

%t mp[n_]:=Module[{prs=Transpose[FactorInteger[n]][[1]],pos},pos= Floor[ Length[ prs]/2]+1;prs[[pos]]]; mp/@Select[Range[300],OddQ[PrimeNu[#]]&] (* _Harvey P. Dale_, Jun 20 2012 *)

%Y Cf. A030230

%K nonn

%O 1,1

%A _Leroy Quet_, Mar 16 2010

%E More terms from _R. J. Mathar_, Oct 09 2010