On trying to exceed θ(P(n+1)) with θ(k) where k is prime(n) smooth.

A363061, A363844, and A363794.
Written by Michael Thomas De Vlieger, St. Louis, Missouri, 2023 0623.

Abstract.

Primorials P(n) represent local minima of Euler’s totient φ(n) and occur among local maxima of the regular counting function θ(n) = A010846(n). In the latter case, this has to do with the expansion of the bounded regular tensor in scope and rank. The least nondivisor prime q₁ has outsized impact on θ(n). Therefore we are led to consider a sequence of smallest prime(n) smooth k such that θ(k) is at least as large as θ(P(n+1)).

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Concerns OEIS sequences:

A000005, A000010, A000040, A002110, A010846, A038566, A053669, A363061, A363844, A363794.

To cite:

Michael Thomas De Vlieger, On trying to exceed θ(P(n+1)) with θ(k) where k is prime(n) smooth, Simple Sequence Analysis, Article 20230623.