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Numbers n such that n^5 + 3 is semiprime.
2

%I #9 Aug 20 2019 02:17:00

%S 1,2,4,6,11,14,18,19,24,31,32,38,40,46,50,55,59,70,74,76,84,92,96,100,

%T 115,119,128,139,148,150,151,154,155,158,164,178,184,200,203,204,206,

%U 210,230,236,238,239,242,248,256,263,272,278,284,295,299,304,306,310

%N Numbers n such that n^5 + 3 is semiprime.

%C Note that n^5 + 3 is irreducible over integers, unlike n^5 + 1 as in A104238.

%e 1^5 + 3 = 4 = 2 * 2

%e 2^5 + 3 = 35 = 5 * 7

%e 4^5 + 3 = 1027 = 13 * 79

%e 6^5 + 3 = 7779 = 3 * 2593

%e 11^5 + 3 = 161054 = 2 * 80527

%e 14^5 + 3 = 89 * 6043

%e 100^5 + 3 = 10000000003 = 7 * 1428571429

%e 1000^5 + 3 = 1000000000000003 = 14902357 * 67103479

%e 1000000^5 + 3 = 1000000000000000000000000000003 = 1859827 * 537684419034673655130289.

%p with(numtheory): a:=proc(n) if bigomega(n^5+3)=2 then n else fi end: seq(a(n),n=1..400); # _Emeric Deutsch_, Jul 16 2005

%t Select[Range[400],PrimeOmega[#^5+3]==2&] (* _Harvey P. Dale_, Jul 16 2017 *)

%Y Cf. A104238, A108814.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jul 12 2005

%E More terms from _Emeric Deutsch_, Jul 16 2005