A276632 Integer part of the geometric mean of the prime factors of n.

1, 2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 3, 3, 2, 17, 2, 19, 3, 4, 4, 23, 2, 5, 5, 3, 3, 29, 3, 31, 2, 5, 5, 5, 2, 37, 6, 6, 3, 41, 3, 43, 4, 3, 6, 47, 2, 7, 3, 7, 5, 53, 2, 7, 3, 7, 7, 59, 3, 61, 7, 4, 2, 8, 4, 67, 5, 8, 4, 71, 2, 73, 8, 3, 6, 8, 4, 79, 3

Offset: 1

Author

R. J. Mathar, Sep 08 2016

Keywords

• nonn

Examples

			For n=20, the two distinct prime factors are 2 and 5, the arithmetic mean is sqrt(2*5), and the integer part is a(20)=3.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A079866 (primes with multiplicity)

Programs

Maple

A276632 := proc(n)
    floor(root[A001221(n)](A007947(n))) ;
end proc:
seq(A276632(n),n=1..80) ;

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger@n); Table[Floor[(rad[n])^(1/PrimeNu[n])], {n, 1, 50}] (* G. C. Greubel, May 19 2017 *)

Formula

a(n) = floor( A007947(n)^(1/A001221(n)) ).