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A104479
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Positive integers n such that n^16 + 1 is semiprime (A001358).
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4
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3, 4, 9, 12, 14, 16, 18, 20, 26, 29, 40, 41, 48, 58, 70, 73, 81, 87, 92, 96, 104, 111, 113, 114, 118, 122, 130, 140, 142, 144, 146, 150, 157, 162, 164, 167, 168, 172, 173, 184, 187, 192, 194, 195, 199, 200, 202, 208, 220, 230, 232, 244, 253, 256, 266, 278, 292, 295, 298
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| n^16 + 1 is an irreducible polynomial over Z and thus can be either prime (A006313) or semiprime.
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FORMULA
| a(n)^16 + 1 is semiprime (A001358).
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EXAMPLE
| 3^16 + 1 = 43046722 = 2 * 21523361,
4^16 + 1 = 4294967297 = 641 * 6 700417,
9^16 + 1 = 1853020188851842 = 2 * 926510094425921,
12^16 + 1 = 184884258895036417 = 153953 * 1200913648289,
200^16 + 1 = 6553600000000000000000000000000000001 =
162123499503471553 * 40423504427621041217.
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MATHEMATICA
| Select[Range[300], PrimeOmega[#^16+1]==2&] (* From Harvey P. Dale, Aug 21 2011 *)
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PROG
| (MAGMA)IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [2..300]|IsSemiprime(n^16+1)][From V. Librandi, Dec 21 2010]
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CROSSREFS
| Cf. A000040, A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237.
Sequence in context: A182828 A035256 A047075 * A067163 A010394 A010427
Adjacent sequences: A104476 A104477 A104478 * A104480 A104481 A104482
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 18 2005
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EXTENSIONS
| More terms from Vincenzo Librandi, Dec 21 2010
Corrected (adding 202, 208, and 220) by Harvey P. Dale, Aug 21 2011
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