cp's OEIS Frontend

A167690 The even composites c such that c=q*g*j*y and q+g=j*y where q,g,j,y are primes.

%I A167690 #14 Mar 02 2025 16:03:31
%S A167690 16,54,126,210,250,390,462,686,798,1150,1254,1794,1870,2046,2662,2886,
%T A167690 3162,3458,4394,4606,4930,5830,5934,8246,8602,9246,9430,9826,10974,
%U A167690 13718,14110,15370,15762,16198,19434,21414,22678,24198,24334,25990
%N A167690 The even composites c such that c=q*g*j*y and q+g=j*y where q,g,j,y are primes.
%H A167690 Karl-Heinz Hofmann, <a href="/A167690/b167690.txt">Table of n, a(n) for n = 1..10000</a>
%e A167690 a(1) = 2 * 2 * 2 * 2 =  16
%e A167690 a(2) = 3 * 3 * 2 * 3 =  54
%e A167690 a(3) = 2 * 7 * 3 * 3 = 126
%e A167690 a(4) = 3 * 7 * 2 * 5 = 210.
%o A167690 (Python)
%o A167690 from sympy import isprime, nextprime, integer_nthroot
%o A167690 c_upto = 100000
%o A167690 A167690, q, lim_q, lim_g = set(), 2, integer_nthroot(c_upto//2,3)[0], integer_nthroot(c_upto//3,2)[0]//2
%o A167690 while (g:=q) <= lim_q:
%o A167690     while g <= lim_g:
%o A167690         fac = 2 * q * g
%o A167690         for j in [2 * q - g, 2 * g - q, q * g - 2 ]:
%o A167690             if isprime(j) and (an:= fac * j) < c_upto : A167690.add(an)
%o A167690         g = nextprime(g)
%o A167690     q = nextprime(q)
%o A167690 print((A167690:=sorted(A167690))) # _Karl-Heinz Hofmann_, Feb 21 2025
%Y A167690 Cf. A000040, A157931, A167629.
%K A167690 nonn
%O A167690 1,1
%A A167690 _Juri-Stepan Gerasimov_, Nov 09 2009
%E A167690 Corrected (250, 686, 1794 etc inserted, 9486, 15782 removed) by _R. J. Mathar_, May 30 2010