A273291 A273289(n)^Omega(n), where Omega = A001222.

2, 3, 4, 5, 9, 7, 8, 9, 25, 11, 8, 13, 25, 25, 16, 17, 27, 19, 8, 25, 49, 23, 16, 25, 121, 27, 8, 29, 27, 31, 32, 49, 121, 49, 81, 37, 121, 121, 16, 41, 27, 43, 8, 27, 169, 47, 32, 49, 125, 121, 8, 53, 81, 121, 16, 121, 289, 59, 81, 61, 289, 27, 64, 121, 27, 67, 8, 169, 125

Offset: 2

Author

Giuseppe Coppoletta, May 25 2016

Keywords

• nonn

Comments

a(n)>= A273290(n).

a(n) is by definition the power of a prime. It coincides with n iff n is also a power of prime (A246655).

Examples

			a(308) = 5^4 because Omega(308)=4 and the median of [2, 2, 7, 11] is (2+7)/2 = 4.5, whose next prime is 5. See A273290 for other examples.
		

Links

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

Crossrefs

Cf. A273285, A273289, A273290, A079871, A001222, A246655.

Programs

Mathematica

Table[If[PrimeQ@ #, #, NextPrime@ #] &[Median@ #]^Length@ # &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ n, 1], {n, 2, 70}] (* Michael De Vlieger, May 27 2016 *)

Sage

def r(n): return [f[0] for f in factor(n) for _ in range(f[1])]
[next_prime(ceil(median(r(n)))-1)^sloane.A001222(n) for n in (2..70)]

Formula

a(n) = A273289(n)^A001222(n).