A281192 Numbers with no squarefree neighbors.

17, 19, 26, 49, 51, 53, 55, 89, 91, 97, 99, 125, 127, 149, 151, 161, 163, 170, 197, 199, 233, 235, 241, 243, 244, 249, 251, 269, 271, 293, 295, 305, 307, 337, 339, 341, 343, 349, 351, 362, 377, 379, 413, 415, 424, 449, 451, 476, 485, 487, 489, 491, 521, 523, 530, 549, 551, 557, 559, 577

Offset

1,1

Comments

Includes all n == 17 or 19 (mod 36), also 2*p^2-1 and 2*p^2+1 for odd primes p. - Robert Israel, Jan 17 2017

This sequence has density around 0.106.... - Charles R Greathouse IV, Jan 23 2017

More accurately, the asymptotic density of this sequence is 1 - 2/zeta(2) + Product_{p prime} (1 - 2/p^2) = 1 - 2 * A059956 + A065474 = 0.1067798952... - Amiram Eldar, Feb 25 2021

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

17 is in this sequence because 17 - 1 = 16 = 2^4 and 17 + 1 = 18 = 2*3^2 are not squarefree.

Maple

select(t -> not numtheory:-issqrfree(t-1) and not numtheory:-issqrfree(t+1), [$1..1000]); # Robert Israel, Jan 17 2017

Mathematica

Select[Range[600], !SquareFreeQ[# - 1] && !SquareFreeQ[# + 1] &] (* Vincenzo Librandi, Jan 17 2017 *)

Prog

(Magma) [n: n in [2..600] | not IsSquarefree(n-1) and not IsSquarefree(n+1)];
(PARI) is(n)=!issquarefree(n-1) && !issquarefree(n+1) \\ Charles R Greathouse IV, Jan 23 2017

Crossrefs

Supersequence of A075432 and A235578.

Cf. A005117, A059956, A065474, A280892.

Sequence in context: A334287 A249566 A205646 * A073247 A133347 A096990

Adjacent sequences: A281189 A281190 A281191 * A281193 A281194 A281195

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jan 16 2017

Status

approved