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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 January 16 23:43 EST 2022. Contains 350377 sequences. (Running on oeis4.)