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A167690
The even composites c such that c=q*g*j*y and q+g=j*y where q,g,j,y are primes.
1
16, 54, 126, 210, 250, 390, 462, 686, 798, 1150, 1254, 1794, 1870, 2046, 2662, 2886, 3162, 3458, 4394, 4606, 4930, 5830, 5934, 8246, 8602, 9246, 9430, 9826, 10974, 13718, 14110, 15370, 15762, 16198, 19434, 21414, 22678, 24198, 24334, 25990
OFFSET
1,1
LINKS
EXAMPLE
a(1) = 2 * 2 * 2 * 2 = 16
a(2) = 3 * 3 * 2 * 3 = 54
a(3) = 2 * 7 * 3 * 3 = 126
a(4) = 3 * 7 * 2 * 5 = 210.
PROG
(Python)
from sympy import isprime, nextprime, integer_nthroot
c_upto = 100000
A167690, q, lim_q, lim_g = set(), 2, integer_nthroot(c_upto//2, 3)[0], integer_nthroot(c_upto//3, 2)[0]//2
while (g:=q) <= lim_q:
while g <= lim_g:
fac = 2 * q * g
for j in [2 * q - g, 2 * g - q, q * g - 2 ]:
if isprime(j) and (an:= fac * j) < c_upto : A167690.add(an)
g = nextprime(g)
q = nextprime(q)
print((A167690:=sorted(A167690))) # Karl-Heinz Hofmann, Feb 21 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected (250, 686, 1794 etc inserted, 9486, 15782 removed) by R. J. Mathar, May 30 2010
STATUS
approved