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A075109 Odd perfect powers (1 together with numbers m^k, m odd, k >= 2). 11
1, 9, 25, 27, 49, 81, 121, 125, 169, 225, 243, 289, 343, 361, 441, 529, 625, 729, 841, 961, 1089, 1225, 1331, 1369, 1521, 1681, 1849, 2025, 2187, 2197, 2209, 2401, 2601, 2809, 3025, 3125, 3249, 3375, 3481, 3721, 3969, 4225, 4489, 4761, 4913, 5041, 5329, 5625 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = 1 + Sum_{k>=2} mu(k)*(1-zeta(k)*(2^k-1)/2^k) = 1.2890375574... - Amiram Eldar, Dec 19 2020
MAPLE
q:= n-> n=1 or n::odd and igcd(seq(i[2], i=ifactors(n)[2]))>1:
select(q, [$1..6000])[]; # Alois P. Heinz, May 04 2022
MATHEMATICA
Take[Union[Flatten[Table[a^b, {a, 1, 99, 2}, {b, 2, 15}]]], 50] (* Alonso del Arte, Nov 22 2011 *)
PROG
(Haskell)
a075109 n = a075109_list !! (n-1)
a075109_list = filter odd a001597_list -- Reinhard Zumkeller, Oct 04 2012
(Magma) [1] cat [n : n in [3..6000 by 2] | IsPower(n) ]; // Vincenzo Librandi, Mar 31 2014
(PARI) isok(m) = (m==1) || ((m%2) && ispower(m)); \\ Michel Marcus, May 04 2022
CROSSREFS
Intersection of A001597 and A005408.
Sequence in context: A275196 A325373 A062739 * A319165 A319152 A244623
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Oct 11 2002
EXTENSIONS
Definition clarified by N. J. A. Sloane, Dec 25 2021
STATUS
approved

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Last modified May 29 10:54 EDT 2024. Contains 372938 sequences. (Running on oeis4.)