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URL: https://oeis.org/A073247

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A073247
Squarefree numbers k such that k-1 and k+1 are not squarefree.
29
17, 19, 26, 51, 53, 55, 89, 91, 97, 127, 149, 151, 161, 163, 170, 197, 199, 233, 235, 241, 249, 251, 269, 271, 293, 295, 305, 307, 337, 339, 341, 349, 362, 377, 379, 413, 415, 449, 451, 485, 487, 489, 491, 521, 523, 530, 551, 557, 559, 577, 579, 593, 595
OFFSET
1,1
COMMENTS
Probably 11*n < a(n) < 12*n for n > 189. - Charles R Greathouse IV, Nov 05 2017
The asymptotic density of this sequence is 1/zeta(2) - 2 * Product_{p prime} (1 - 2/p^2) + Product_{p prime} (1 - 3/p^2) = A059956 - 2*A065474 + A206256 = 0.088145884881346585838... . - Amiram Eldar, Aug 30 2024
LINKS
Christopher E. Thompson, Table of n, a(n) for n = 1..10000
MAPLE
sf:= select(numtheory:-issqrfree, [$1..1000]):
map(t -> `if`(sf[t-1]=sf[t]-1 or sf[t+1]=sf[t]+1, NULL, sf[t]), [$2..nops(sf)-1]); # Robert Israel, Feb 01 2016
MATHEMATICA
Reap[For[n = 0, n <= 1000, n++, If[SquareFreeQ[n] && !SquareFreeQ[n-1] && !SquareFreeQ[n+1], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Feb 26 2019 *)
PROG
(PARI) is(n)=!issquarefree(n-1) && issquarefree(n) && !issquarefree(n+1) \\ Charles R Greathouse IV, Nov 05 2017
(PARI) list(lim)=my(v=List(), l1, l2); forfactored(k=9, lim\1+1, if(!issquarefree(k) && !issquarefree(l2) && issquarefree(l1), listput(v, l1[1])); l2=l1; l1=k); Vec(v) \\ Charles R Greathouse IV, Nov 27 2024
CROSSREFS
Cf. A268331, A268332, A268333, A268334 (squarefree numbers isolated by more than 2, 3, etc.).
Sequence in context: A249566 A205646 A281192 * A133347 A096990 A175384
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 22 2002
STATUS
approved