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A273290
A273288(n)^Omega(n), where Omega = A001222.
4
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
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
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
KEYWORD
nonn
AUTHOR
Giuseppe Coppoletta, May 25 2016
STATUS
approved