A396672 Averages of two consecutive odd squarefree semiprimes p, q (A046388) that share a common factor > 1 with at least one of p and q.

18, 27, 45, 126, 150, 180, 360, 540, 576, 594, 810, 846, 936, 1296, 1323, 2466, 2646, 2850, 3000, 3060, 3186, 3300, 3690, 3834, 3906, 3915, 4050, 4356, 4446, 4464, 4653, 4797, 4824, 5004, 5232, 5796, 5850, 6150, 6264, 6336, 6390, 6426, 6450, 6600, 6714, 6723, 7020

Offset

1,1

Comments

The least terms not divisible by 3 are 127250, 494750, 578830, ... .

Links

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

Example

  j A046388(j)
         (A046388(j)+A046388(j+1))/2
                 Factorizations
                                Terms
  1 15           3 * 5
         18      2 * 3^2       a(1) = 18
  2 21           3 * 7
         27      3^3           a(2) = 27
  3 33           3 * 11
         34      2 * 17
  4 35           5 * 7
         37      37
  5 39           3 * 13
         45      3^2 * 5       a(3) = 45
  6 51           3 * 17
         53      53
  7 55           5 * 11
    ...
    127235       5 * 25447
         127250  2 * 5^3 * 509 a(..) = 127250
    127265       5 * 25453

Prog

(PARI) a396672(upto=7500) = my(p1=15, p2); forstep(k=21, upto, 2, my(f=factor(k), m); if(omega(f)==2 && bigomega(f)==2, p2=k; m=p1+p2; if(gcd(p1, m)!=1 || gcd(p2, m)!=1, print1(m/2, ", ")); p1=p2))
(Python)
from sympy import factorint
def A046388_isok_and_factorization(n):
    return [n % 2 == 1 and (len(f := factorint(n, multiple=True)) == 2 and f[0] != f[1]), f]
A046388, A396672, k = [15], [], 19
while len(A396672) < (aupto := 47):
    k += 2
    if (r:=A046388_isok_and_factorization(k))[0]:
        A046388.append(k)
        if (f := factorint(A046388[-2], multiple=True))[0] in r[1] or f[1] in r[1]:
            A396672.append((A046388[-2] + A046388[-1]) // 2)
print(A396672) # Karl-Heinz Hofmann, Jun 02 2026

Crossrefs

Cf. A046388.

Sequence in context: A345309 A337752 A379146 * A279108 A038632 A138336

Adjacent sequences: A396669 A396670 A396671 * A396673 A396674 A396675

Keyword

nonn

Author

Hugo Pfoertner, Jun 02 2026

Status

approved