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A276632
Integer part of the geometric mean of the prime factors of n.
1
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
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
KEYWORD
nonn
AUTHOR
R. J. Mathar, Sep 08 2016
STATUS
approved