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A120432
Numbers n such that n-1 and n+1 are prime powers.
1
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
1,1
COMMENTS
A generalization of A014574.
LINKS
FORMULA
{2} UNION A088071. - R. J. Mathar, Aug 07 2008
EXAMPLE
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.
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 *)
PROG
(Magma) [2] cat [n : n in [3..1110] | IsPrimePower(n-1) and IsPrimePower(n+1)]; // Vincenzo Librandi, Nov 25 2016
CROSSREFS
Sequence in context: A034287 A067128 A245779 * A020490 A217660 A275581
KEYWORD
nonn
AUTHOR
Greg Huber, Jul 13 2006
EXTENSIONS
More terms from Emeric Deutsch, Stefan Steinerberger and Ryan Propper, Jul 23 2006
STATUS
approved