login
Numbers n such that 3^n + n^3 is a semiprime.
3

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

%S 1,4,8,14,16,22,23,32,34,50,52,62,80,154,170,176,202,208,214,236,248,

%T 332,398,422

%N Numbers n such that 3^n + n^3 is a semiprime.

%C a(25) >= 428. - _Hugo Pfoertner_, Jul 28 2019

%H <a href="http://factordb.com/index.php?query=3%5E428%2B428%5E3">Status of 3^428-428^3 in factordb.com</a>.

%e 4 is OK because 3^4 + 4^3 = 81 + 64 = 145 = 5*29 (semiprime).

%t Select[Range[100], PrimeOmega[3^# + #^3]==2&] (* _Vincenzo Librandi_, May 21 2014 *)

%o (Magma)IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [1..95] | IsSemiprime(3^n+n^3)]; // _Vincenzo Librandi_ Dec 16 2010

%Y Cf. A114970, A114973, A114974.

%K nonn,more,hard

%O 1,2

%A _Zak Seidov_, Feb 22 2006

%E a(14)-a(23) from _Luke March_, Jul 27 2015

%E a(24) from _Hugo Pfoertner_, Jul 28 2019