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A120432
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Numbers n such that n-1 and n+1 are prime powers.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A generalization of A014574.
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FORMULA
| {2} UNION A088071. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2008]
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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.
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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 (deutsch(AT)duke.poly.edu), Jul 23 2006
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MATHEMATICA
| Insert[Select[Range[3, 3000], Length[FactorInteger[ # - 1]] == Length[ FactorInteger[ # + 1]] == 1 &], 2, 1] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jul 23 2006
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CROSSREFS
| Cf. A000961, A014574.
Sequence in context: A074715 A034287 A067128 * A020490 A014875 A029469
Adjacent sequences: A120429 A120430 A120431 * A120433 A120434 A120435
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KEYWORD
| nonn
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AUTHOR
| Greg Huber (huber(AT)alum.mit.edu), Jul 13 2006
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Ryan Propper (rpropper(AT)stanford.edu), Jul 23 2006
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