cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A104479 #14 Sep 08 2022 08:45:17
%S A104479 3,4,9,12,14,16,18,20,26,29,40,41,48,58,70,73,81,87,92,96,104,111,113,
%T A104479 114,118,122,130,140,142,144,146,150,157,162,164,167,168,172,173,184,
%U A104479 187,192,194,195,199,200,202,208,220,230,232,244,253,256,266,278,292,295,298
%N A104479 Positive integers n such that n^16 + 1 is semiprime (A001358).
%C A104479 n^16 + 1 is an irreducible polynomial over Z and thus can be either prime (A006313) or semiprime.
%H A104479 Robert Price, <a href="/A104479/b104479.txt">Table of n, a(n) for n = 1..102</a>
%F A104479 a(n)^16 + 1 is semiprime (A001358).
%e A104479 3^16 + 1 = 43046722 = 2 * 21523361,
%e A104479 4^16 + 1 = 4294967297 = 641 * 6 700417,
%e A104479 9^16 + 1 = 1853020188851842 = 2 * 926510094425921,
%e A104479 12^16 + 1 = 184884258895036417 = 153953 * 1200913648289,
%e A104479 200^16 + 1 = 6553600000000000000000000000000000001 =
%e A104479 162123499503471553 * 40423504427621041217.
%t A104479 Select[Range[300],PrimeOmega[#^16+1]==2&] (* _Harvey P. Dale_, Aug 21 2011 *)
%t A104479 Select[Range[1000], 2 == Total[Transpose[FactorInteger[#^16 + 1]][[2]]] &] (* _Robert Price_, Mar 11 2015 *)
%o A104479 (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
%Y A104479 Cf. A006313, A001358, A085722, A096173, A186669, A104238, A103854, A105041, A105066, A105078, A105122, A105142, A105237, A104335, A104479, A104494, A104657, A105282.
%K A104479 easy,nonn
%O A104479 1,1
%A A104479 _Jonathan Vos Post_, Apr 18 2005
%E A104479 More terms from _Vincenzo Librandi_, Dec 21 2010
%E A104479 Corrected (adding 202, 208, and 220) by _Harvey P. Dale_, Aug 21 2011