A079866 a(1)=1 and for n>1: floor(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

1, 2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 3, 3, 2, 17, 2, 19, 2, 4, 4, 23, 2, 5, 5, 3, 3, 29, 3, 31, 2, 5, 5, 5, 2, 37, 6, 6, 2, 41, 3, 43, 3, 3, 6, 47, 2, 7, 3, 7, 3, 53, 2, 7, 2, 7, 7, 59, 2, 61, 7, 3, 2, 8, 4, 67, 4, 8, 4, 71, 2, 73, 8, 4, 4, 8, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 9, 4, 9, 9, 9, 2

Offset: 1

Author

Reinhard Zumkeller, Jan 13 2003

Keywords

• nonn

Comments

a(n) <= A079868(n).

A020639(n) <= a(n) <= A006530(n);

a(m) = A079868(m) = A079870(m) iff m is a prime power (A000961).

Links

• David W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

A079867(n) = a(n)^A001222(n).

Cf. A079747, A358890.

Programs

Maple

A079866 := proc(n)
    root[numtheory[bigomega](n)](n) ;
    floor(%) ;
end proc:
seq(A079866(n),n=1..97) ; # R. J. Mathar, Sep 07 2016

Mathematica

Join[{1}, Table[Floor[n^(1/PrimeOmega[n])], {n, 2, 20}]] (* G. C. Greubel, Sep 16 2016 *)

PARI

a(n) = if (n==1, 1, sqrtnint(n, bigomega(n))); \\ Michel Marcus, Sep 09 2016