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URL: https://oeis.org/A356873

⇱ A356873 - OEIS

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A356873
a(n) is the smallest number k such that 2^k+1 has at least n distinct prime factors.
0
0, 5, 14, 18, 30, 42, 78, 78, 78, 90, 150, 150, 210, 210, 234, 234, 270, 390, 390, 390, 390, 450, 510, 630, 630, 630, 810, 810, 810, 966, 966, 1170, 1170, 1170, 1170, 1170, 1170, 1170
OFFSET
1,2
COMMENTS
From Jon E. Schoenfield, Sep 04 2022: (Start)
a(39) <= a(40) <= a(41) <= 1530.
a(42) <= a(43) <= a(44) <= 1890.
a(45) <= a(46) <= 2070.
a(47) <= a(48) <= ... <= a(54) = 2730. (End)
MATHEMATICA
a[n_] := Block[{k=0}, While[ Length@ FactorInteger[2^k + 1] < n, k++]; k]; Array[a, 12] (* Giovanni Resta, Oct 13 2022 *)
PROG
(Python)
from sympy import factorint, isprime
from itertools import count, islice
def f(n): return 1 if isprime(n) else len(factorint(n))
def agen():
n = 1
for k in count(0):
v = f(2**k+1)
while v >= n: yield k; n += 1
print(list(islice(agen(), 10))) # Michael S. Branicky, Sep 02 2022
(PARI) a(n) = my(k=1); while (omega(2^k+1) < n, k++); k; \\ Michel Marcus, Sep 05 2022
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Alex Ratushnyak, Sep 02 2022
EXTENSIONS
a(11)-a(38) from Michael S. Branicky, Sep 02 2022 using A071852
STATUS
approved