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%I #17 Mar 06 2024 15:47:09
%S 216,1728,46656,74088,157464,216000,287496,373248,474552,592704,
%T 729000,884736,1061208,1259712,1481544,2299968,2628072,2985984,
%U 3375000,3796416,4251528,5832000,6434856,7762392,8489664,9261000,10077696,10941048,11852352,12812904,13824000,16003008,17173512,19683000
%N Cubes sandwiched between squarefree numbers.
%C All terms are multiples of 216.
%e 216 = 2^3 * 3^3 is a cube; 215 = 5 * 43 and 217 = 7 * 31 are squarefree, so 216 is a term.
%e 1728 = 2^6 * 3^3 is a cube; 1727 = 11 * 157 and 1729 = 7 * 13 * 19 are squarefree, so 1728 is a term.
%e 46656 = 2^6 * 3^6 is a cube; 46655 = 5 * 7 * 31 * 43 and 46657 = 13 * 37 * 97 are squarefree, so 46656 is a term.
%t Select[Range[270]^3, And @@ SquareFreeQ /@ (# + {-1, 1}) &] (* _Amiram Eldar_, Feb 27 2024 *)
%Y Cf. A005117. Subsequence of A000578.
%K nonn
%O 1,1
%A _Massimo Kofler_, Feb 27 2024