A076469 Perfect powers m^k where k >= 5.

1, 32, 64, 128, 243, 256, 512, 729, 1024, 2048, 2187, 3125, 4096, 6561, 7776, 8192, 15625, 16384, 16807, 19683, 32768, 46656, 59049, 65536, 78125, 100000, 117649, 131072, 161051, 177147, 248832, 262144, 279936, 371293, 390625, 524288, 531441

Offset

1,2

Comments

If p|n when at least p^5|n.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Sum_{n>=1} 1/a(n) = 4 - zeta(2) - zeta(3) - zeta(4) + Sum_{k>=2} mu(k)*(4 - zeta(k) - zeta(2*k) - zeta(3*k) - zeta(4*k)) = 1.06932853458... . - Amiram Eldar, Dec 03 2022

Mathematica

a = {1}; Do[ If[ Apply[ GCD, Last[ Transpose[ FactorInteger[n]]]] > 4, a = Append[a, n]; Print[n]], {n, 2, 537823}]; a

Crossrefs

Cf. A001597, A076467, A076468, A076470.

Cf. A002117, A013661, A013662.

Sequence in context: A144908 A172419 A069492 * A256819 A358250 A235057

Adjacent sequences: A076466 A076467 A076468 * A076470 A076471 A076472

Keyword

nonn

Author

Robert G. Wilson v, Oct 14 2002

Status

approved