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).

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

1,2

Comments

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).

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Mathematica

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

Prog

(PARI) a(n) = if (n==1, 1, my(b=bigomega(n)); sqrtnint(n, b)^b); \\ Michel Marcus, Feb 16 2026

Crossrefs

Cf. A000961, A020639, A006530, A068794, A068795, A079869, A079866, A079871.

Sequence in context: A373735 A377487 A273284 * A273290 A079869 A200322

Adjacent sequences: A079864 A079865 A079866 * A079868 A079869 A079870

Keyword

nonn

Author

Reinhard Zumkeller, Jan 13 2003

Status

approved