A079868 -id:A079868 - cp's OEIS frontend

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

Reinhard Zumkeller, Jan 13 2003

nonn

a(n) <= A079868(n).
A020639(n) <= a(n) <= A006530(n);
a(m) = A079868(m) = A079870(m) iff m is a prime power (A000961).

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

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

Cf. A079747, A358890.

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

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

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

A079869 a(1)=1 and for n>1: round(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

Original entry on oeis.org

1, 2, 3, 4, 5, 4, 7, 8, 9, 9, 11, 8, 13, 16, 16, 16, 17, 27, 19, 27, 25, 25, 23, 16, 25, 25, 27, 27, 29, 27, 31, 32, 36, 36, 36, 16, 37, 36, 36, 81, 41, 27, 43, 64, 64, 49, 47, 32, 49, 64, 49, 64, 53, 81, 49, 81, 64, 64, 59, 81, 61, 64, 64, 64, 64, 64, 67, 64, 64, 64, 71, 32, 73

Offset: 1

Reinhard Zumkeller, Jan 13 2003

nonn

A079867(n)<=a(n)<=A079869(n); A020639(n)<=a(n)<=A006530(n);

a(m)=m=A079867(m)=A079871(m) iff m is a prime power (A000961).

a(n)=A079868(n)^A001222(n). Cf. A079872, A068794, A068795.

ron[n_]:=Module[{c=PrimeOmega[n]},Round[n^(1/c)]^c]; Join[{1},Array[ ron,80,2]] (* Harvey P. Dale, Jun 17 2020 *)

A079870 a(1)=1 and for n>1: ceiling(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

Original entry on oeis.org

1, 2, 3, 2, 5, 3, 7, 2, 3, 4, 11, 3, 13, 4, 4, 2, 17, 3, 19, 3, 5, 5, 23, 3, 5, 6, 3, 4, 29, 4, 31, 2, 6, 6, 6, 3, 37, 7, 7, 3, 41, 4, 43, 4, 4, 7, 47, 3, 7, 4, 8, 4, 53, 3, 8, 3, 8, 8, 59, 3, 61, 8, 4, 2, 9, 5, 67, 5, 9, 5, 71, 3, 73, 9, 5, 5, 9, 5, 79, 3, 3, 10, 83, 4, 10, 10, 10, 4, 89, 4, 10, 5, 10

Offset: 1

Reinhard Zumkeller, Jan 13 2003

nonn

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A001222, A006530, A020639, A068794, A068795, A079869, A079871.

A079870[n_] := If [n == 1, 1, Ceiling[n^(1/PrimeOmega[n])]];
Array[A079870, 100] (* Paolo Xausa, Oct 28 2024 *)

a(n) = if (n==1, 1, ceil(n^(1/bigomega(n)))); \\ Michel Marcus, May 31 2016

A079871(n) = a(n)^A001222(n).
a(n) >= A079868(n); A020639(n) <= a(n) <= A006530(n);
a(m) = A079868(m) iff m is a prime power (A000961).

cp's OEIS Frontend

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).

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A079869 a(1)=1 and for n>1: round(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

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A079870 a(1)=1 and for n>1: ceiling(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

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