

A157987


Smallest roots m of perfect powers (m^k where m is an integer and k >= 2) multiplied by 1 when m is prime (m^k thus a prime power).


1



1, 2, 2, 3, 2, 5, 3, 2, 6, 7, 2, 3, 10, 11, 5, 2, 12, 13, 14, 6, 15, 3, 2, 17, 18, 7, 19, 20, 21, 22, 2, 23, 24, 5, 26, 3, 28, 29, 30, 31, 10, 2, 33, 34, 35, 6, 11, 37, 38, 39, 40, 41, 12, 42, 43, 44, 45, 2, 46, 3, 13, 47, 48, 7, 50, 51, 52
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OFFSET

1,2


LINKS

Daniel Forgues, Table of n, a(n) for n=1..10000


FORMULA

a(n) = {m}_n * (1)^{Pi(m)  Pi(m1)}
where {m}_n is the smallest root of {m^k}_n (the nth perfect power with positive integer base m corresponding to largest integer exponent k) and Pi(m) is the prime counting function evaluated at m.
a(n) = m * (1)^{Pi(m)  Pi(m1)}, with m = A025478(n) = {A001597(n)}^{1/{A025479(n)}}.


CROSSREFS

Cf. A157985 Perfect powers (m^k where m is an integer and k >= 2) multiplied by 1 when m is prime for largest k (m^k thus a prime power).
Cf. A157986 Largest exponents of perfect powers (m^k where m is an integer and k >= 2) multiplied by 1 when base m is prime (m^k thus a prime power).
Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
Cf. A025479 Largest exponents of perfect powers (A001597).
Cf. A025478 Least roots of perfect powers (A001597).
Sequence in context: A254269 A264662 A076403 * A025478 A084371 A025476
Adjacent sequences: A157984 A157985 A157986 * A157988 A157989 A157990


KEYWORD

sign


AUTHOR

Daniel Forgues, Mar 10 2009, Mar 14 2009


STATUS

approved



