Observation on primorials

[David Wilson]

Let f be a multiplicative function with

f(p) > f(p^k) > 1 (p prime, k > 1)
f(p) > f(q) > 1 (p, q prime, p < q)

then the record maxima of f occur at n# for n >= 1.

Similarly, if

0 < f(p) < f(p^k) < 1 (p prime, k > 1)
0 < f(p) < f(q) < 1 (p, q prime, p < q).

Then the record minima of f occur at n# for n >= 1.

Not deep theorems, but not well known and definite time-savers.

Might be worth noting on A002110.
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