A079869 -id:A079869 - cp's OEIS frontend

A079871 a(1)=1 and for n>1: ceiling(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

1, 2, 3, 4, 5, 9, 7, 8, 9, 16, 11, 27, 13, 16, 16, 16, 17, 27, 19, 27, 25, 25, 23, 81, 25, 36, 27, 64, 29, 64, 31, 32, 36, 36, 36, 81, 37, 49, 49, 81, 41, 64, 43, 64, 64, 49, 47, 243, 49, 64, 64, 64, 53, 81, 64, 81, 64, 64, 59, 81, 61, 64, 64, 64, 81, 125, 67, 125, 81, 125, 71

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, A079870.

A079871[n_] := If [n == 1, 1, Ceiling[n^(1/#)]^# & [PrimeOmega[n]]];
Array[A079871, 100] (* Paolo Xausa, Oct 27 2024 *)

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

a(n) = A079870(n)^A001222(n).
a(n) >= A079869(n); A020639(n) <= a(n) <= A006530(n);
a(m) = m = A079869(m) iff m is a prime power (A000961).

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).

A079867 a(1)=1 and for n>1: floor(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, 9, 9, 16, 17, 8, 19, 8, 16, 16, 23, 16, 25, 25, 27, 27, 29, 27, 31, 32, 25, 25, 25, 16, 37, 36, 36, 16, 41, 27, 43, 27, 27, 36, 47, 32, 49, 27, 49, 27, 53, 16, 49, 16, 49, 49, 59, 16, 61, 49, 27, 64, 64, 64, 67, 64, 64, 64, 71, 32, 73, 64

Offset: 1

Reinhard Zumkeller, Jan 13 2003

nonn

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

a(m)=m=A079869(m)=A079871(m) iff m is a prime power (A000961).

a(n)=A079866(n)^A001222(n), cf. A068794, A068795.

Join[{1},Table[Floor[n^(1/PrimeOmega[n])]^PrimeOmega[n],{n,2,80}]] (* Harvey P. Dale, May 19 2018 *)

A079868 a(1)=1 and for n>1: round(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, 2, 7, 2, 3, 3, 11, 2, 13, 4, 4, 2, 17, 3, 19, 3, 5, 5, 23, 2, 5, 5, 3, 3, 29, 3, 31, 2, 6, 6, 6, 2, 37, 6, 6, 3, 41, 3, 43, 4, 4, 7, 47, 2, 7, 4, 7, 4, 53, 3, 7, 3, 8, 8, 59, 3, 61, 8, 4, 2, 8, 4, 67, 4, 8, 4, 71, 2, 73, 9, 4, 4, 9, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 10, 5, 10, 10

Offset: 1

Reinhard Zumkeller, Jan 13 2003

nonn

A079866(n)<=a(n)<=A079870(n); A020639(n)<=a(n)<=A006530(n);

a(m)=A079866(m)=A079870(m) iff m is a prime power (A000961).

Cf. A079869(n)=a(n)^A001222(n), A079881.

Join[{1},Table[Floor[n^(1/PrimeOmega[n])+1/2],{n,2,100}]] (* Harvey P. Dale, Aug 11 2012 *)

A079872 a(1)=0, a(n) = signum(round(n^(1/Omega(n)))^Omega(n) - n), where Omega(n) is the total number of prime factors of n (A001222).

Original entry on oeis.org

0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, 1, -1, 0, -1, -1, 1, 0, -1, 0, 1, 1, 1, 0, -1, 0, 1, -1, 1, 0, 1, -1, 1, 1, 1, 0, 1, 0, 1, 1, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, 1, -1, -1, 1, -1, 0, -1, 0, -1, 0, -1, -1, -1, -1, -1, 0, -1, 1, 1, 1, 1, 1, -1

Offset: 1

Reinhard Zumkeller, Jan 13 2003

a(m) = 0 iff m is a prime power (A000961).

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

Cf. A000961, A001222, A057427, A079869.

A079872[n_] := If[n == 1, 0, Sign[Round[n^(1/#)]^# - n] & [PrimeOmega[n]]];
Array[A079872, 100] (* Paolo Xausa, Sep 02 2025 *)

a(n) = A057427(A079869(n) - n).

cp's OEIS Frontend

A079871 a(1)=1 and for n>1: ceiling(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A079867 a(1)=1 and for n>1: floor(n^(1/Omega(n)))^Omega(n), where Omega(n) is the total number of prime factors of n (A001222).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A079868 a(1)=1 and for n>1: round(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A079872 a(1)=0, a(n) = signum(round(n^(1/Omega(n)))^Omega(n) - n), where Omega(n) is the total number of prime factors of n (A001222).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula