A273284 A273282(n)^Omega(n), where Omega = A001222.

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

Offset: 2

Author

Giuseppe Coppoletta, May 20 2016

Keywords

• nonn

Comments

a(n) <= A079867(n) for any n>=2.

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

Examples

			a(33) = 25 because Omega(33)=2 and 5^2 < 33 < 7^2.
If n= 3^3 * 31^2 * 67 then a(n)= 7^6 and A273285(n)=11^6 because Omega(n)=6 and 7^6 < n < 11^6.
		

Links

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

Crossrefs

Cf. A273282, A273285, A273290, A079867, A246655, A001222.

Programs

Mathematica

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

PARI

a(n) = my(bn=bigomega(n)); precprime(sqrtnint(n, bn))^bn; \\ Michel Marcus, May 24 2016

Sage

s=sloane.A001222; [previous_prime(floor(n^(1/s(n)))+1)^s(n) for n in (2..74)]

Formula

a(n) = A273282(n)^A001222(n).