
COMMENTS

Presumably there are no further terms.
From Hal M. Switkay, Nov 04 2019: (Start)
1. a(n+1) is the product of the first n terms of A328852.
2. This sequence is most rapidly constructed as the intersection of A095849 and A224078. It is designed to list all potential solutions to a question. Let n be a natural number, k real <= 0, e real > 0. Let P(n,k,e) state: on the domain of natural numbers, sigma_k(x)/x^e reaches a maximum at x = n. This implies Q(n,k): sigma_k(n) > sigma_k(m) for m < n a natural number. We ask: for which natural numbers n is it true for all real k <= 0 that there is a real e > 0 such that P(n,k,e)?
If any such n exist, they must belong to the present sequence. A095849 consists of all natural numbers n such that for all real k <= 0, Q(n,k) holds. A224078 consists of all natural numbers n such that for some real e0 and e1 both > 0, P(n,0,e0) and P(n,1,e1) hold. It would be interesting to see the list of n for which there is an e2 > 0 such that P(n,2,e2) holds.
Conjecture: the solutions to this problem, if any, form an initial sequence of the present sequence. (End)
Every term of this sequence is also in A065385: a record for the cototient function.  Hal M. Switkay, Feb 27 2021
Every term of this sequence, except the first, is also in A210594: factordense numbers.  Hal M. Switkay, Mar 29 2021
