A362333 Least nonnegative integer k such that (gpf(n)!)^k is divisible by n, where gpf(n) is the greatest prime factor of n.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 3, 1, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1

Offset

1,4

Comments

First differs from A088388 at n = 40.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) > 1 if and only if n is in A057109.

a(n) <= A051903(n).

a(n) = ceiling(A371148(n)/A371149(n)). - Pontus von Brömssen, Mar 16 2024

Example

For n = 12, gpf(n)! = 3! = 6 is not divisible by 12, but (3!)^2 = 36 is divisible by 12, so a(12) = 2.

Prog

(Python)
from sympy import factorint
def A362333(n):
    f = factorint(n)
    gpf = max(f, default=None)
    a = 0
    for p in f:
        m = gpf
        v = 0
        while m >= p:
            m //= p
            v += m
        a = max(a, -(-f[p]//v))
    return a

Crossrefs

Cf. A006530, A051903, A057109, A088388, A371148, A371149, A371151, A371152.

Sequence in context: A302045 A302035 A307907 * A371148 A088388 A070013

Adjacent sequences: A362330 A362331 A362332 * A362334 A362335 A362336

Keyword

nonn

Author

Pontus von Brömssen, Apr 16 2023

Status

approved