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%I #16 Jun 03 2016 15:00:54
%S 2,3,4,5,4,7,8,9,9,11,8,13,9,9,16,17,27,19,8,25,25,23,16,25,49,27,8,
%T 29,27,31,32,49,49,25,16,37,49,49,16,41,27,43,8,27,121,47,32,49,125,
%U 49,8,53,81,49,16,121,169,59,16,61,169,27,64,49,27,67,8,169,125
%N A273288(n)^Omega(n), where Omega = A001222.
%C a(n) is by definition the power of a prime. It coincides with n iff n is the power of a prime (A246655).
%C a(n) <= A273291(n)
%H Giuseppe Coppoletta, <a href="/A273290/b273290.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A273288(n)^A001222(n).
%e a(70) = A273291(70) = 5^3 because the median of its prime factors [2, 5, 7] is the central value 5 (prime) and Omega(70)=3.
%e a(308) = 3^4 because Omega(308)=4 and the median of [2, 2, 7, 11] is (2+7)/2 = 4.5, whose previous prime is 3.
%t Table[Prime[PrimePi@ Median@ #]^Length@ # &@ Flatten@ Apply[Table[#1 {#2}] &, FactorInteger@ n, 1], {n, 2, 75}] (* _Michael De Vlieger_, May 27 2016 *)
%o (Sage) def pfwr(n): return flatten([([p] * m) for (p, m) in factor(n)]) # (list of prime factors of n with repetition)
%o [previous_prime(floor(median(pfwr(n)))+1)^sloane.A001222(n) for n in (2..70)]
%Y Cf. A273284, A273288, A273291, A079867, A246655, A001222.
%K nonn
%O 2,1
%A _Giuseppe Coppoletta_, May 25 2016
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