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A356873 a(n) is the smallest number k such that 2^k+1 has at least n distinct prime factors.

%I A356873 #27 Oct 13 2022 09:50:58
%S A356873 0,5,14,18,30,42,78,78,78,90,150,150,210,210,234,234,270,390,390,390,
%T A356873 390,450,510,630,630,630,810,810,810,966,966,1170,1170,1170,1170,1170,
%U A356873 1170,1170
%N A356873 a(n) is the smallest number k such that 2^k+1 has at least n distinct prime factors.
%C A356873 From _Jon E. Schoenfield_, Sep 04 2022: (Start)
%C A356873 a(39) <= a(40) <= a(41) <= 1530.
%C A356873 a(42) <= a(43) <= a(44) <= 1890.
%C A356873 a(45) <= a(46) <= 2070.
%C A356873 a(47) <= a(48) <= ... <= a(54) = 2730. (End)
%t A356873 a[n_] := Block[{k=0}, While[ Length@ FactorInteger[2^k + 1] < n, k++]; k]; Array[a, 12] (* _Giovanni Resta_, Oct 13 2022 *)
%o A356873 (Python)
%o A356873 from sympy import factorint, isprime
%o A356873 from itertools import count, islice
%o A356873 def f(n): return 1 if isprime(n) else len(factorint(n))
%o A356873 def agen():
%o A356873     n = 1
%o A356873     for k in count(0):
%o A356873         v = f(2**k+1)
%o A356873         while v >= n: yield k; n += 1
%o A356873 print(list(islice(agen(), 10))) # _Michael S. Branicky_, Sep 02 2022
%o A356873 (PARI) a(n) = my(k=1); while (omega(2^k+1) < n, k++); k; \\ _Michel Marcus_, Sep 05 2022
%Y A356873 Cf. A046799, A071852.
%Y A356873 Cf. A180278, A219108, A356872.
%K A356873 nonn,hard,more
%O A356873 1,2
%A A356873 _Alex Ratushnyak_, Sep 02 2022
%E A356873 a(11)-a(38) from _Michael S. Branicky_, Sep 02 2022 using A071852