A392162 - OEIS

%I #25 Jan 12 2026 14:29:18

%S 2,30,154,60,182,66,70,78,105,102,110,42,130,84,165,114,140,132,170,

%T 126,190,138,195,168,220,156,230,174,231,90,238,120,266,150,273,180,

%U 286,186,255,198,260,204,280,222,285,234,290,228,308,240

%N a(n) is the smallest number not yet in the sequence that has exactly one prime factor in common with a(n-1) and has at least two other different prime factors that are not factors of a(n-1); a(1) = 2.

%H Michael S. Branicky, <a href="/A392162/b392162.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 30 since it shares the prime 2 with a(1) = 2 and has two other different primes not contained in a(1) (3 and 5).

%e a(3) = 154 = 2*7*11 since it shares the prime 2 with a(2) = 30 and has two other different primes not contained in a(2) (7 and 11).

%o (Python)

%o from sympy import factorint

%o from functools import cache

%o from itertools import count, islice

%o @cache

%o def pf(n): return set(factorint(n))

%o def cond(pfan, pfk): return len(pfk&pfan) == 1 and len(pfk-pfan) >= 2

%o def agen():

%o     an, aset, m = 2, {2}, 3

%o     while True:

%o         yield an

%o         pfan = pf(an)

%o         m = next(k for k in count(m) if k not in aset and len(pf(k)) >= 3)

%o         an = next(k for k in count(m) if k not in aset and cond(pfan, pf(k)))

%o         aset.add(an)

%o print(list(islice(agen(), 55))) # _Michael S. Branicky_, Jan 06 2026

%Y Cf. A064413, A350352.

%K nonn

%O 1,1

%A _Enrique Navarrete_, Jan 01 2026