

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).


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



FORMULA

a(n) = {m^k}_n * (1)^(Pi(m)  Pi(m1)) where {m^k}_n is 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.


CROSSREFS

Cf. A001597 (perfect powers), A025479 (largest exponents of perfect powers.
Cf. A025478 (least roots of perfect powers).


KEYWORD

sign


AUTHOR



STATUS

approved



