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

1,1

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

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

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

Cf. A013939, A065474, A115170.

Sequence in context: A008213 A008187 A274595 * A081935 A008006 A081937

Adjacent sequences: A115225 A115226 A115227 * A115229 A115230 A115231

Keyword

easy,nonn

Author

Don Reble, Mar 05 2006

Extensions

Corrected by Zak Seidov, Oct 21 2016

Status

approved