A108868 Numbers n such that n^5 + 3 is semiprime.

1, 2, 4, 6, 11, 14, 18, 19, 24, 31, 32, 38, 40, 46, 50, 55, 59, 70, 74, 76, 84, 92, 96, 100, 115, 119, 128, 139, 148, 150, 151, 154, 155, 158, 164, 178, 184, 200, 203, 204, 206, 210, 230, 236, 238, 239, 242, 248, 256, 263, 272, 278, 284, 295, 299, 304, 306, 310

Offset: 1

Author

Jonathan Vos Post, Jul 12 2005

Keywords

• easy
• nonn

Comments

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

Examples

			1^5 + 3 = 4 = 2 * 2
2^5 + 3 = 35 = 5 * 7
4^5 + 3 = 1027 = 13 * 79
6^5 + 3 = 7779 = 3 * 2593
11^5 + 3 = 161054 = 2 * 80527
14^5 + 3 = 89 * 6043
100^5 + 3 = 10000000003 = 7 * 1428571429
1000^5 + 3 = 1000000000000003 = 14902357 * 67103479
1000000^5 + 3 = 1000000000000000000000000000003 = 1859827 * 537684419034673655130289.
		

Crossrefs

Cf. A104238, A108814.

Programs

Maple

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

Mathematica

Select[Range[400],PrimeOmega[#^5+3]==2&] (* Harvey P. Dale, Jul 16 2017 *)

Extensions

More terms from Emeric Deutsch, Jul 16 2005