A356593 Smallest k such that primorial(k) > n^2.

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Author

Christoph B. Kassir, Aug 14 2022

Keywords

• nonn

Crossrefs

Cf. A337769, A002110, A000290.

Programs

Mathematica

a[n_] := Module[{k = 1, prod = p = 2}, While[prod < n^2, p = NextPrime[p]; prod *= p; k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 15 2022 *)

Python

from sympy import primorial
def a(n):
    k = 1
    while True:
        if primorial(k) > n**2:
            return(k)
        k += 1
for n in range(1, 90):
    print(f'{a(n)}, ', end='')