A167690 The even composites c such that c=q*g*j*y and q+g=j*y where q,g,j,y are primes.
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
Keywords
Examples
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.
Links
- Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000
Programs
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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
Extensions
Corrected (250, 686, 1794 etc inserted, 9486, 15782 removed) by R. J. Mathar, May 30 2010