

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

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 FellerTornier 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



