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A281192 Numbers with no squarefree neighbors. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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, 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

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)