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A115228 Nonsquarefree numbers n such that 2n+1 is also nonsquarefree (A013929). 2
4, 12, 24, 40, 49, 60, 76, 84, 112, 121, 144, 148, 162, 171, 175, 180, 184, 212, 220, 256, 264, 292, 312, 328, 364, 387, 400, 412, 416, 420, 423, 436, 472, 480, 490, 508, 512, 544, 580, 612, 616, 625, 637, 652, 684, 688, 712, 722, 724, 760, 796, 808, 812 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For any distinct primes p, q with q odd, contains all n such that n == 0 (mod p^2) and n == -1/2 (mod q^2). - Robert Israel, Oct 21 2016
LINKS
FORMULA
a(n) ~ n/(1 - 14/Pi^2 + 3*k/2 ) as n -> infinity, where k is the Feller-Tornier constant (A065474). - Robert Israel, Oct 21 2016
EXAMPLE
24 is in the sequence because 2^2 divides 24 and 7^2 divides 24*2 + 1.
MAPLE
select(n -> not numtheory:-issqrfree(n) and not numtheory:-issqrfree(2*n+1), [$1..2000]); # Robert Israel, Oct 21 2016
MATHEMATICA
fQ[n_] := ! SquareFreeQ[n] && ! SquareFreeQ[2 n + 1]; Select[Range[1000], fQ] (* Robert G. Wilson v, Oct 21 2016 *)
PROG
(PARI) isok(n) = !issquarefree(n) && ! issquarefree(2*n+1); \\ Michel Marcus, Oct 22 2016
CROSSREFS
Sequence in context: A008213 A008187 A274595 * A081935 A008006 A081937
KEYWORD
easy,nonn
AUTHOR
Don Reble, Mar 05 2006
EXTENSIONS
Corrected by Zak Seidov, Oct 21 2016
STATUS
approved

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Last modified February 23 15:29 EST 2024. Contains 370283 sequences. (Running on oeis4.)