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A328549 1, together with the numbers that are simultaneously superior highly composite (A002201), colossally abundant (A004490), deeply composite (A095848), and miserable average divisor numbers (A263572). 1
1, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

REFERENCES

Hal M. Switkay, Email to N. J. A. Sloane, Oct 20 2019

LINKS

Table of n, a(n) for n=1..12.

CROSSREFS

1 together with the intersection of A002201, A004490, A095848, A263572.

Cf. A095849, A224078, A328852, A210594.

Sequence in context: A328450 A322381 A265125 * A002201 A263572 A004490

Adjacent sequences:  A328546 A328547 A328548 * A328550 A328551 A328552

KEYWORD

nonn,fini,full

AUTHOR

N. J. A. Sloane, Oct 20 2019

STATUS

approved

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Last modified November 29 06:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)