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Numbers n such that 7^n + n^7 is a semiprime.
4

%I #28 Sep 08 2022 08:45:23

%S 2,12,16,18,30,39,160,214,235,408

%N Numbers n such that 7^n + n^7 is a semiprime.

%C 627 and 748 are sequence terms < 1100. a(11) >= 510. Unknown factorization also for 622 and 790. - _Hugo Pfoertner_, Jul 28 2019

%H <a href="http://factordb.com/index.php?query=7%5E510%2B510%5E7">Status of 7^510-510^7 in factordb.com</a>.

%e 2 is in the sequence because 7^2 + 2^7 = 177 = 3*59 (semiprime).

%e 12 is in the sequence because 7^12 + 12^7 = 13*1067470693 (semiprime). [_Vincenzo Librandi_, Dec 16 2010]

%o (Magma)IsSemiprime:=func<n | &+[k[2]: k in Factorization(n)] eq 2>; [n: n in [1..85] | IsSemiprime(7^n+n^7)] // _Vincenzo Librandi_, Dec 16 2010

%Y Cf. A114970, A114971, A114973.

%K nonn,more,hard

%O 1,1

%A _Zak Seidov_, Feb 22 2006

%E Corrected (inserted 12) from _Vincenzo Librandi_, Dec 16 2010

%E a(7) from _D. S. McNeil_, Dec 16 2010

%E a(8)-a(10) from _Luke March_, Aug 03 2015