cp's OEIS Frontend

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: factor-dense numbers. - Hal M. Switkay, Mar 29 2021

This sequence is to A210594 (the generalization in the latter's comment section) as sigma (A000203, the sum of divisors function) is to tau (A000005, the number of divisors function).