A115228 -id:A115228 - cp's OEIS frontend

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

Jonathan Vos Post, Mar 03 2006

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

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

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

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

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

Edited by Don Reble, Mar 05 2006

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

cp's OEIS Frontend

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

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