A120432 Numbers n such that n-1 and n+1 are prime powers.

2, 3, 4, 6, 8, 10, 12, 18, 24, 26, 28, 30, 42, 48, 60, 72, 80, 82, 102, 108, 126, 138, 150, 168, 180, 192, 198, 228, 240, 242, 270, 282, 312, 348, 360, 420, 432, 462, 522, 570, 600, 618, 642, 660, 728, 810, 822, 828, 840, 858, 882, 1020, 1032, 1050, 1062, 1092

Offset: 1

Author

Greg Huber, Jul 13 2006

Keywords

• nonn

Comments

A generalization of A014574.

Examples

			10 is in the sequence because both 9 and 11 are prime powers; 26 is in the sequence because both 25 and 27 are prime powers.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000961, A014574.

Programs

Magma

[2] cat [n : n in [3..1110] | IsPrimePower(n-1) and  IsPrimePower(n+1)]; // Vincenzo Librandi, Nov 25 2016

Maple

with(numtheory): a:=proc(n) if nops(factorset(n-1))*nops(factorset(n+1))=1 then n else fi end: 2,seq(a(n),n=2..1500); # Emeric Deutsch, Jul 23 2006

Mathematica

Insert[Select[Range[3, 3000], Length[FactorInteger[ # - 1]] == Length[ FactorInteger[ # + 1]] == 1 &], 2, 1] (* Stefan Steinerberger, Jul 23 2006 *)
Join[{2}, Select[Range[1100], And @@ PrimePowerQ /@ {# - 1, # + 1} &]] (* Ivan Neretin, Nov 24 2016 *)

Formula

{2} UNION A088071. - R. J. Mathar, Aug 07 2008

Extensions

More terms from Emeric Deutsch, Stefan Steinerberger and Ryan Propper, Jul 23 2006