A112774 Semiprimes of the form 6n+4.

4, 10, 22, 34, 46, 58, 82, 94, 106, 118, 142, 166, 178, 202, 214, 226, 262, 274, 298, 334, 346, 358, 382, 394, 454, 466, 478, 502, 514, 526, 538, 562, 586, 622, 634, 694, 706, 718, 766, 778, 802, 838, 862, 886, 898, 922, 934, 958, 982, 1006, 1018, 1042, 1114

Offset: 1

Author

Jonathan Vos Post and Ray Chandler, Oct 15 2005

Keywords

• easy
• nonn

Comments

{6} + A112772 + A112774 = A100484 = 2*A000040.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

IsSemiprime:=func; [s: n in [0..200] | IsSemiprime(s) where s is 6*n + 4]; // Vincenzo Librandi, Sep 22 2012

Mathematica

Select[6 Range[0, 200] + 4, PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 22 2012 *)

Python

from sympy import factorint
def semiprime(n): f = factorint(n); return sum(f[p] for p in f) == 2
print(list(filter(semiprime, range(4, 1115, 6)))) # Michael S. Branicky, Apr 10 2021

Formula

a(n) = 2 * A003627(n) = 6 * A024893(n) + 4.