|
%I #32 May 04 2022 11:06:42
%S 4,8,16,32,36,64,100,128,144,196,216,256,324,400,484,512,576,676,784,
%T 900,1000,1024,1156,1296,1444,1600,1728,1764,1936,2048,2116,2304,2500,
%U 2704,2744,2916,3136,3364,3600,3844,4096,4356,4624,4900,5184,5476,5776,5832
%N Even perfect powers: numbers of the form (2*m)^k for some m>=1 and k>=2.
%H Reinhard Zumkeller, <a href="/A075090/b075090.txt">Table of n, a(n) for n = 1..10000</a>
%F Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/2^k = 0.5854268109... - _Amiram Eldar_, Dec 19 2020
%p q:= n-> n::even 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, 2, 100, 2}, {b, 2, 15}]]], 50] (* _Alonso del Arte_, Nov 22 2011 *)
%o (Haskell)
%o a075090 n = a075090_list !! (n-1)
%o a075090_list = filter even a001597_list -- _Reinhard Zumkeller_, Oct 04 2012
%o (PARI) isok(m) = !(m%2) && ispower(m); \\ _Michel Marcus_, May 03 2022
%Y Intersection of A005843 and A001597.
%Y Cf. A008683, A075109.
%K easy,nonn
%O 1,1
%A _Zak Seidov_, Oct 11 2002
%E Name formula corrected by _Kevin Ryde_, May 04 2022
|
