A356872 a(n) = k is the smallest number such that 3*k+1 contains n distinct prime factors.

1, 3, 23, 303, 4363, 56723, 1077743, 33410043, 718854803, 22284498903, 824526459423, 35454637755203, 1588862487308763, 68321086954276823, 4167586304210886223, 213640038906023626563, 13032042373267441220363, 873146839008918561764343, 63739719247651055008797063

Offset: 1

Author

Alex Ratushnyak, Sep 02 2022

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 1..349

Crossrefs

Cf. A002110, A180278, A219108.

Programs

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(3*k+1)
        while v >= n: yield k; n += 1
print(list(islice(agen(), 7))) # Michael S. Branicky, Sep 02 2022

Formula

From Michael S. Branicky, Sep 02 2022: (Start)

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

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)

Extensions

a(8) from Michael S. Branicky, Sep 02 2022

a(9)-a(19) from Jon E. Schoenfield, Sep 02 2022