



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, 29, 27, 31, 32, 49, 49, 25, 16, 37, 49, 49, 16, 41, 27, 43, 8, 27, 121, 47, 32, 49, 125, 49, 8, 53, 81, 49, 16, 121, 169, 59, 16, 61, 169, 27, 64, 49, 27, 67, 8, 169, 125
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OFFSET

2,1


COMMENTS

a(n) is by definition the power of a prime. It coincides with n iff n is the power of a prime (A246655).
a(n) <= A273291(n)


LINKS

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


FORMULA

a(n) = A273288(n)^A001222(n).


EXAMPLE

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.
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.


MATHEMATICA

Table[Prime[PrimePi@ Median@ #]^Length@ # &@ Flatten@ Apply[Table[#1 {#2}] &, FactorInteger@ n, 1], {n, 2, 75}] (* Michael De Vlieger, May 27 2016 *)


PROG

(Sage) def pfwr(n): return flatten([([p] * m) for (p, m) in factor(n)]) # (list of prime factors of n with repetition)
[previous_prime(floor(median(pfwr(n)))+1)^sloane.A001222(n) for n in (2..70)]


CROSSREFS

Cf. A273284, A273288, A273291, A079867, A246655, A001222.
Sequence in context: A074882 A273284 A079867 * A079869 A200322 A075054
Adjacent sequences: A273287 A273288 A273289 * A273291 A273292 A273293


KEYWORD

nonn


AUTHOR

Giuseppe Coppoletta, May 25 2016


STATUS

approved



