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%I #39 Sep 08 2022 08:45:07
%S 1,9,25,27,49,81,121,125,169,225,243,289,343,361,441,529,625,729,841,
%T 961,1089,1225,1331,1369,1521,1681,1849,2025,2187,2197,2209,2401,2601,
%U 2809,3025,3125,3249,3375,3481,3721,3969,4225,4489,4761,4913,5041,5329,5625
%N Odd perfect powers (1 together with numbers m^k, m odd, k >= 2).
%H Reinhard Zumkeller, <a href="/A075109/b075109.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%p q:= n-> n=1 or n::odd and igcd(seq(i[2], i=ifactors(n)[2]))>1:
%p select(q, [$1..6000])[]; # _Alois P. Heinz_, May 04 2022
%t Take[Union[Flatten[Table[a^b, {a, 1, 99, 2}, {b, 2, 15}]]], 50] (* _Alonso del Arte_, Nov 22 2011 *)
%o (Haskell)
%o a075109 n = a075109_list !! (n-1)
%o a075109_list = filter odd a001597_list -- _Reinhard Zumkeller_, Oct 04 2012
%o (Magma) [1] cat [n : n in [3..6000 by 2] | IsPower(n) ]; // _Vincenzo Librandi_, Mar 31 2014
%o (PARI) isok(m) = (m==1) || ((m%2) && ispower(m)); \\ _Michel Marcus_, May 04 2022
%Y Intersection of A001597 and A005408.
%Y Cf. A008683, A075090.
%K easy,nonn
%O 1,2
%A _Zak Seidov_, Oct 11 2002
%E Definition clarified by _N. J. A. Sloane_, Dec 25 2021
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