A104479 Positive integers n such that n^16 + 1 is semiprime (A001358).

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

Robert Price, Table of n, a(n) for n = 1..102

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

Crossrefs

Cf. A006313, A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.

Sequence in context: A287400 A309758 A047075 * A067163 A287450 A010394

Adjacent sequences: A104476 A104477 A104478 * A104480 A104481 A104482

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