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(Python)
from math import prod
from sympy import divisors, factorint
def A359411(n): return prod(sum(1 for d in divisors(e, generator=True) if e|d == e) for e in factorint(n).values()) # Chai Wah Wu, Sep 01 2023
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Amiram Eldar, <a href="/A359411/b359411.txt">Table of n, a(n) for n = 1..10000</a>
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a(8) = 2 since 8 has 2 divisors that are both infinitary and exponential: 2 and 8.