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a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors.
2

%I #30 Sep 28 2022 11:16:39

%S 1,3,23,303,4363,56723,1077743,33410043,718854803,22284498903,

%T 824526459423,35454637755203,1588862487308763,68321086954276823,

%U 4167586304210886223,213640038906023626563,13032042373267441220363,873146839008918561764343,63739719247651055008797063

%N a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors.

%H David A. Corneth, <a href="/A356872/b356872.txt">Table of n, a(n) for n = 1..349</a>

%F From _Michael S. Branicky_, Sep 02 2022: (Start)

%F a(n) >= ceiling((A002110(n)-1)/3).

%F a(n) <= (c*A002110(n+1)/3-1)/3 for n > 1, and c = 1 or 2 chosen so the expression is an integer, with equality holding for c = 1 for n = 2, 3, 6, 7, ... . (End)

%o (Python)

%o from sympy import factorint, isprime

%o from itertools import count, islice

%o def f(n): return 1 if isprime(n) else len(factorint(n))

%o def agen():

%o n = 1

%o for k in count(0):

%o v = f(3*k+1)

%o while v >= n: yield k; n += 1

%o print(list(islice(agen(), 7))) # _Michael S. Branicky_, Sep 02 2022

%Y Cf. A002110, A180278, A219108.

%K nonn

%O 1,2

%A _Alex Ratushnyak_, Sep 02 2022

%E a(8) from _Michael S. Branicky_, Sep 02 2022

%E a(9)-a(19) from _Jon E. Schoenfield_, Sep 02 2022