A175264 a(n) = the middle prime among the distinct primes dividing {the n-th positive integer divisible by exactly an odd number of distinct primes}.

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, 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, 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

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A030230

Sequence in context: A133684 A286151 A192138 * A025473 A351847 A192141

Adjacent sequences: A175261 A175262 A175263 * A175265 A175266 A175267

Keyword

nonn

Author

Leroy Quet, Mar 16 2010

Extensions

More terms from R. J. Mathar, Oct 09 2010

Status

approved