A167629 The odd composites c such that c=q*g*j*y/2 and q+g=j*y where q,g,j,y are distinct primes.

105, 195, 231, 399, 627, 897, 935, 1023, 1443, 1581, 1729, 2465, 2915, 2967, 4123, 4301, 4623, 4715, 5487, 7055, 7685, 7881, 8099, 9717, 10707, 11339, 12099, 12995, 14993, 16377, 16383, 17353, 17423, 19599, 20213, 20915, 23779, 24963, 25327

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 07 2009

Keywords

• nonn

Examples

			a(1) =  3 *  7 *  5 = 105 (q=3, g= 7, j=2, y=5)
a(2) = 13 *  3 *  5 = 195 (q=2, g=13, j=3, y=5)
a(3) =  3 * 11 *  7 = 231 (q=3, g=11, j=2, y=7)
a(4) = 19 *  3 *  7 = 329 (q=2, g=19, j=3, y=7)
a(5) =  3 * 19 * 11 = 627 (q=3, g=19, j=2, y=11)
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A157931.

Programs

Python

from sympy import primerange, primepi
k_upto = 25327
A167629, primeset = set(), set(primelist:= list(primerange(3, int(k_upto**0.5)+1)))
for x in range (primepi(k_upto**(1/3))):
    limit, y = k_upto // (a:=primelist[x]), x
    while (b:= primelist[(y:=y+1)]) * (c1:=(a * b - 2)) <= limit:
        if c1 in primeset : A167629.add(a * b * c1)
        if (c2 := b * 2 - a) in primeset : A167629.add(a * b * c2)
    y -= 1
    while (b:= primelist[(y:=y+1)]) * (c2:=(b * 2 - a)) <= limit:
        if c2 in primeset : A167629.add(a * b * c2)
print(A167629:=sorted(A167629)) # Karl-Heinz Hofmann, Jan 30 2025

Extensions

Corrected and extended by D. S. McNeil, Dec 10 2009