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

1,1

Links

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

Example

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)

Prog

(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

Crossrefs

Cf. A000040, A157931.

Sequence in context: A161962 A046887 A026066 * A326141 A347881 A044337

Adjacent sequences: A167626 A167627 A167628 * A167630 A167631 A167632

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 07 2009

Extensions

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

Status

approved