A269758 Prime powers with squarefree neighbors.

2, 4, 16, 32, 128, 256, 2048, 8192, 16384, 65536, 131072, 524288, 4194304, 8388608, 33554432, 67108864, 268435456, 536870912, 2147483648, 4294967296, 17179869184, 34359738368, 137438953472, 274877906944, 2199023255552, 8796093022208, 17592186044416, 70368744177664

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 30 2016

Keywords

• nonn

Comments

All a(n) are powers of 2.

No terms are powers of 8. - Robert Israel, Jan 07 2019

Examples

			2 is in this sequence because both 2 - 1 = 1 and 2 + 1 = 3 are squarefree.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A000961.

Programs

Magma

[2^n: n in [1..50] | IsSquarefree(2^n-1) and IsSquarefree(2^n+1)];

Maple

map(t -> 2^t, select(t -> numtheory:-issqrfree(2^t-1) and numtheory:-issqrfree(2^t+1), [seq(seq(3*k+i,i=1..2),k=0..20)])); # Robert Israel, Jan 07 2019