A321070 Squares divisible by more than one cube > 1.

64, 256, 576, 729, 1024, 1296, 1600, 2304, 2916, 3136, 4096, 5184, 6400, 6561, 7744, 9216, 10000, 10816, 11664, 12544, 14400, 15625, 16384, 18225, 18496, 20736, 23104, 25600, 26244, 28224, 30976, 32400, 33856, 35721, 36864, 38416, 40000, 43264, 46656, 50176

Offset

1,1

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Formula

From Amiram Eldar, Jun 25 2022: (Start)

Equals A000290 \ (union of A062503 and A320965).

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

Example

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

Mathematica

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

Prog

(PARI) iscubes(n) = {my(nb = 0); fordiv(n, d, if ((d>1) && ispower(d, 3), nb++; if (nb > 1, return(1))); ); }
isok(n) = issquare(n) && iscubes(n); \\ Michel Marcus, Oct 27 2018

Crossrefs

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

Sequence in context: A223315 A263924 A236331 * A017066 A141478 A107262

Adjacent sequences: A321067 A321068 A321069 * A321071 A321072 A321073

Keyword

nonn

Author

Hugo Pfoertner, Oct 27 2018

Status

approved