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).

1, -4, -8, -9, -16, -25, -27, -32, 36, -49, -64, -81, 100, -121, -125, -128, 144, -169, 196, 216, 225, -243, -256, -289, 324, -343, -361, 400, 441, 484, -512, -529, 576, -625, 676, -729, 784, -841, 900, -961, 1000, -1024, 1089, 1156, 1225, 1296, -1331

Offset

1,2

Comments

The rather strange phrase "largest k" in the definition refers to the fact that there can be several ways to write a number in the form m^k. - N. J. A. Sloane, Jan 01 2019

Links

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

Formula

a(n) = {m^k}_n * (-1)^(Pi(m) - Pi(m-1)) where {m^k}_n is 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) = A001597(n) * (-1)^(Pi(m) - Pi(m-1)), with m = A001597(n)^(1/A025479(n)).

Crossrefs

Cf. A001597 (perfect powers), A025479 (largest exponents of perfect powers).

Cf. A025478 (least roots of perfect powers).

Cf. A157986.

Sequence in context: A377821 A377846 A317102 * A001597 A359493 A072777

Adjacent sequences: A157982 A157983 A157984 * A157986 A157987 A157988

Keyword

sign,changed

Author

Daniel Forgues, Mar 10 2009

Status

approved