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 A233409 Squares with squarefree neighbors. 1
 4, 16, 36, 144, 196, 256, 400, 484, 900, 1156, 1296, 1600, 1764, 2704, 2916, 3136, 3364, 3600, 4356, 5184, 6084, 7056, 7396, 7744, 8100, 8464, 8836, 9216, 10404, 10816, 11236, 11664, 12100, 12544, 12996, 16384, 16900, 19044, 19600, 20164, 20736, 22500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are multiples of 4. Whether n is congruent to 1 or 3 mod 4, n^2 is congruent to 1 mod 3 and therefore mu(n^2 - 1) = 0. - Alonso del Arte, Dec 12 2013 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 36 is in this sequence because 35 and 37 are both squarefree. 64 is not in this sequence because 63 = 3^2 * 7. MATHEMATICA Select[Table[n^2, {n, 150}], SquareFreeQ[# - 1] && SquareFreeQ[# + 1] &] (* Vaclav Kotesovec, Dec 11 2013 *) Select[Range[150]^2, Abs[MoebiusMu[# - 1] MoebiusMu[# + 1]] == 1 &] (* Alonso del Arte, Dec 11 2013 *) PROG (PARI) forstep(n=2, 1e3, [2, 2, 6, 2, 2, 2, 2], if(issquarefree(n-1) && issquarefree(n+1) && issquarefree(n^2+1), print1(n^2", "))) \\ Charles R Greathouse IV, Mar 18 2014 CROSSREFS Cf. A000290, A005117, A088068. Sequence in context: A075408 A206981 A318149 * A181795 A277285 A136404 Adjacent sequences: A233406 A233407 A233408 * A233410 A233411 A233412 KEYWORD nonn AUTHOR Irina Gerasimova, Dec 09 2013 STATUS approved

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Last modified June 3 11:24 EDT 2023. Contains 363110 sequences. (Running on oeis4.)