A273285 A273283(n)^Omega(n), where Omega = A001222.

2, 3, 4, 5, 9, 7, 8, 9, 25, 11, 27, 13, 25, 25, 16, 17, 27, 19, 27, 25, 25, 23, 81, 25, 49, 27, 125, 29, 125, 31, 32, 49, 49, 49, 81, 37, 49, 49, 81, 41, 125, 43, 125, 125, 49, 47, 243, 49, 125, 121, 125, 53, 81, 121, 81, 121, 121, 59, 81, 61, 121, 125, 64, 121, 125, 67, 125, 121, 125, 71

Offset: 2

Author

Giuseppe Coppoletta, May 20 2016

Keywords

• nonn

Comments

a(n) >= A079871(n) for any n>=2.

a(n) = n iff n is the power of a prime (A246655).

Examples

			a(33) = 49 because Omega(33)=2 and 5^2 < 33 < 7^2.
a(2403) = 11^4 (and A273284(2403)=7^4) because A001222(3^3*89)=4 and 7^4 < n < 11^4.
		

Links

• Giuseppe Coppoletta, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A273283, A273284, A273291, A079871, A001222, A246655.

Programs

Mathematica

Table[NextPrime[(Ceiling[n^(1/PrimeOmega[n])] - 1)]^PrimeOmega[n], {n,2,50}] (* G. C. Greubel, May 26 2016 *)

Sage

s=sloane.A001222; [next_prime(ceil(n^(1/s(n)))-1)^s(n) for n in (2..82)]

Formula

a(n) = A273283(n)^A001222(n).