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

1,2

Comments

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

Links

Table of n, a(n) for n=1..58.

Example

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.

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 *)

Crossrefs

Cf. A104238, A108814.

Sequence in context: A171865 A344622 A068059 * A274261 A156913 A238483

Adjacent sequences: A108865 A108866 A108867 * A108869 A108870 A108871

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 12 2005

Extensions

More terms from Emeric Deutsch, Jul 16 2005

Status

approved