A115170 Non-cubefree numbers k such that 2k+1 is also non-cubefree (A046099).

40, 256, 312, 472, 688, 904, 1120, 1200, 1312, 1336, 1552, 1768, 1984, 2187, 2200, 2312, 2416, 2456, 2632, 2848, 2875, 3064, 3280, 3312, 3429, 3496, 3712, 3928, 3944, 4144, 4312, 4360, 4576, 4792, 5008, 5224, 5312, 5440, 5562, 5656, 5872, 6088, 6250, 6304, 6312, 6345, 6520, 6655, 6688, 6736, 6952

Offset

1,1

Comments

The probability that a random integer is cubefree is 1/zeta(3) (see A088453).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..700 from R. J. Mathar)

Example

312 is there because 2^3 divides 312 and 5^3 divides 312*2+1.

Mathematica

noncfQ[n_] := AnyTrue[FactorInteger[n][[;; , 2]], # > 2 &]; Select[Range[7000], noncfQ[#] && noncfQ[2*# + 1] &] (* Amiram Eldar, May 25 2025 *)

Crossrefs

Cf. A005384 (n and 2n+1 prime), A046099, A088453, A111153 (n and 2n+1 semiprime), A117204 (n and 2n+1 squarefree), A115228.

Sequence in context: A229632 A223426 A290127 * A374240 A247406 A229588

Adjacent sequences: A115167 A115168 A115169 * A115171 A115172 A115173

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 03 2006

Extensions

Edited by Don Reble, Mar 05 2006

2875 inserted by R. J. Mathar, Dec 08 2015

Status

approved