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A104479
Positive integers n such that n^16 + 1 is semiprime (A001358).
13
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
OFFSET
1,1
COMMENTS
n^16 + 1 is an irreducible polynomial over Z and thus can be either prime (A006313) or semiprime.
LINKS
FORMULA
a(n)^16 + 1 is semiprime (A001358).
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.
MATHEMATICA
Select[Range[300], PrimeOmega[#^16+1]==2&] (* Harvey P. Dale, Aug 21 2011 *)
Select[Range[1000], 2 == Total[Transpose[FactorInteger[#^16 + 1]][[2]]] &] (* Robert Price, Mar 11 2015 *)
PROG
(Magma) IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [2..300]|IsSemiprime(n^16+1)] // Vincenzo Librandi, Dec 21 2010
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Apr 18 2005
EXTENSIONS
More terms from Vincenzo Librandi, Dec 21 2010
Corrected (adding 202, 208, and 220) by Harvey P. Dale, Aug 21 2011
STATUS
approved