A115228 Nonsquarefree numbers n such that 2n+1 is also nonsquarefree (A013929).
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
Offset: 1
Examples
24 is in the sequence because 2^2 divides 24 and 7^2 divides 24*2 + 1.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
select(n -> not numtheory:-issqrfree(n) and not numtheory:-issqrfree(2*n+1), [$1..2000]); # Robert Israel, Oct 21 2016
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Mathematica
fQ[n_] := ! SquareFreeQ[n] && ! SquareFreeQ[2 n + 1]; Select[Range[1000], fQ] (* Robert G. Wilson v, Oct 21 2016 *)
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PARI
isok(n) = !issquarefree(n) && ! issquarefree(2*n+1); \\ Michel Marcus, Oct 22 2016
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
Extensions
Corrected by Zak Seidov, Oct 21 2016
Comments