A321070 - OEIS

%I #14 Jun 26 2022 05:52:35

%S 64,256,576,729,1024,1296,1600,2304,2916,3136,4096,5184,6400,6561,

%T 7744,9216,10000,10816,11664,12544,14400,15625,16384,18225,18496,

%U 20736,23104,25600,26244,28224,30976,32400,33856,35721,36864,38416,40000,43264,46656,50176

%N Squares divisible by more than one cube > 1.

%H Hugo Pfoertner, <a href="/A321070/b321070.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Jun 25 2022: (Start)

%F Equals A000290 \ (union of A062503 and A320965).

%F Sum_{n>=1} 1/a(n) = Pi^2/6 - (15/Pi^2) * (1 + Sum_{k>=2} (-1)^k * P(2*k)) = 0.029082273527998239268... . (End)

%e a(1) = 64 because 16^2 is divisible by 2^3 and by 4^3.

%t Select[Range[225]^2, Max[(e = FactorInteger[#][[;; , 2]])] > 4 || (Length[e] > 1 && Sort[e, Greater][[2]] > 2) &] (* _Amiram Eldar_, Jun 25 2022 *)

%o (PARI) iscubes(n) = {my(nb = 0); fordiv(n, d, if ((d>1) && ispower(d, 3), nb++; if (nb > 1, return(1))););}

%o isok(n) = issquare(n) && iscubes(n); \\ _Michel Marcus_, Oct 27 2018

%Y Cf. A000290, A000578, A062503, A062320, A216427, A320965.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Oct 27 2018