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

%I A273291 #16 Jun 03 2016 15:01:55
%S A273291 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,
%T A273291 8,29,27,31,32,49,121,49,81,37,121,121,16,41,27,43,8,27,169,47,32,49,
%U A273291 125,121,8,53,81,121,16,121,289,59,81,61,289,27,64,121,27,67,8,169,125
%N A273291 A273289(n)^Omega(n), where Omega = A001222.
%C A273291 a(n)>= A273290(n).
%C A273291 a(n) is by definition the power of a prime. It coincides with n iff n is also a power of prime (A246655).
%H A273291 Giuseppe Coppoletta, <a href="/A273291/b273291.txt">Table of n, a(n) for n = 2..10000</a>
%F A273291 a(n) = A273289(n)^A001222(n).
%e A273291 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.
%t A273291 Table[If[PrimeQ@ #, #, NextPrime@ #] &[Median@ #]^Length@ # &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ n, 1], {n, 2, 70}] (* _Michael De Vlieger_, May 27 2016 *)
%o A273291 (Sage) def r(n): return [f[0] for f in factor(n) for _ in range(f[1])]
%o A273291 [next_prime(ceil(median(r(n)))-1)^sloane.A001222(n) for n in (2..70)]
%Y A273291 Cf. A273285, A273289, A273290, A079871, A001222, A246655.
%K A273291 nonn
%O A273291 2,1
%A A273291 _Giuseppe Coppoletta_, May 25 2016