A167690 - OEIS

%I #14 Mar 02 2025 16:03:31

%S 16,54,126,210,250,390,462,686,798,1150,1254,1794,1870,2046,2662,2886,

%T 3162,3458,4394,4606,4930,5830,5934,8246,8602,9246,9430,9826,10974,

%U 13718,14110,15370,15762,16198,19434,21414,22678,24198,24334,25990

%N The even composites c such that c=q*g*j*y and q+g=j*y where q,g,j,y are primes.

%H Karl-Heinz Hofmann, <a href="/A167690/b167690.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2 * 2 * 2 * 2 =  16

%e a(2) = 3 * 3 * 2 * 3 =  54

%e a(3) = 2 * 7 * 3 * 3 = 126

%e a(4) = 3 * 7 * 2 * 5 = 210.

%o (Python)

%o from sympy import isprime, nextprime, integer_nthroot

%o c_upto = 100000

%o A167690, q, lim_q, lim_g = set(), 2, integer_nthroot(c_upto//2,3)[0], integer_nthroot(c_upto//3,2)[0]//2

%o while (g:=q) <= lim_q:

%o     while g <= lim_g:

%o         fac = 2 * q * g

%o         for j in [2 * q - g, 2 * g - q, q * g - 2 ]:

%o             if isprime(j) and (an:= fac * j) < c_upto : A167690.add(an)

%o         g = nextprime(g)

%o     q = nextprime(q)

%o print((A167690:=sorted(A167690))) # _Karl-Heinz Hofmann_, Feb 21 2025

%Y Cf. A000040, A157931, A167629.

%K nonn,changed

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 09 2009

%E Corrected (250, 686, 1794 etc inserted, 9486, 15782 removed) by _R. J. Mathar_, May 30 2010