A070265 Odd powers: numbers n = m^e with e > 1 odd.

1, 8, 27, 32, 64, 125, 128, 216, 243, 343, 512, 729, 1000, 1024, 1331, 1728, 2048, 2187, 2197, 2744, 3125, 3375, 4096, 4913, 5832, 6859, 7776, 8000, 8192, 9261, 10648, 12167, 13824, 15625, 16384, 16807, 17576, 19683, 21952, 24389, 27000

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Odd Powers.

Formula

a(n) ~ n^3. - Charles R Greathouse IV, Apr 20 2015

Sum_{n>=1} 1/a(n) = 1 + Sum_{k>=1} mu(2*k+1)*(1-zeta(2*k+1)) = 1.2479294392... - Amiram Eldar, Dec 21 2020

Maple

N:= 10^6: # to get all terms <= N
{1, seq(seq(a^(2*k+1), k = 1 .. floor((log[a](N)-1)/2)), a=2..floor(N^(1/3)))};
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(%, list)); # Robert Israel, Apr 24 2015

Mathematica

nn = 27000; Join[{1}, Union[Flatten[Table[n^i, {i, Prime[Range[2, PrimePi[Log[2, nn]]]]}, {n, 2, nn^(1/i)}]]]] (* T. D. Noe, Apr 19 2011 *)

Prog

(PARI) is(x)=p=ispower(x); x==1||(p>1&bitand(p, p-1)!=0) \\ Charles R Greathouse IV, Apr 20 2015; corrected by Jeppe Stig Nielsen, Jul 14 2015
(PARI) list(lim)=my(v=List([1])); forstep(e=3, log(lim)\log(2), 2, for(n=2, sqrtnint(lim\1, e), listput(v, n^e))); Set(v) \\ Charles R Greathouse IV, Apr 20 2015

Crossrefs

Cf. A001597, A008683, A097054.

Sequence in context: A070495 A270421 A056729 * A354179 A262675 A102834

Adjacent sequences: A070262 A070263 A070264 * A070266 A070267 A070268

Keyword

nonn,easy

Author

Eric W. Weisstein, May 07 2002

Extensions

Name clarified by Charles R Greathouse IV, Oct 16 2015

Status

approved