1,2

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

a(n) = {m}_n * (-1)^{Pi(m) - Pi(m-1)}

where {m}_n is the smallest root of {m^k}_n (the n_th 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(m-1)}, with m = A025478(n) = {A001597(n)}^{1/{A025479(n)}}.

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: A076396 A076397 A076403 this_sequence A025478 A084371 A025476

Adjacent sequences: A157984 A157985 A157986 this_sequence A157988 A157989 A157990

sign

Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009, Mar 14 2009