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

1,2

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A079866 (primes with multiplicity)

Sequence in context: A273282 A079866 A134332 * A273288 A080210 A126594

Adjacent sequences: A276629 A276630 A276631 * A276633 A276634 A276635

Keyword

nonn

Author

R. J. Mathar, Sep 08 2016

Status

approved