A275026 a(n) is the largest number k such that the sum of divisors of k does not exceed the n-th power of the number of divisors of k.

1, 24, 122522400, 41936006482988380963200, 2818633727625754852693848168481445291030176361088000

Offset

1,2

Comments

Largest number k such that sigma(k) <= tau(k)^n.

a(4) >= 41936006482988380963200.

From Jon E. Schoenfield, Nov 01 2017: (Start)

a(5) >= 2812833572480164685801568964499317649172616193664000;

a(6) >= A002110(49)*2321816378289408000 = 1.934333...*10^107.

(End)

a(6) >= A002110(47) * 117664981274811979008000 = 1.9365109... * 10^107. - Max Alekseyev, Mar 21 2023

Links

Table of n, a(n) for n=1..5.

Example

24 has 8 divisors (1, 2, 3, 4, 6, 8, 12, and 24), and their sum is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60, which does not exceed 8^2 = 64. Every number k > 24 has sigma(k) > tau(k)^2, so a(2) = 24.

Crossrefs

Cf. A000005, A000203, A236021.

Sequence in context: A319900 A172803 A141643 * A297424 A013910 A007458

Adjacent sequences: A275023 A275024 A275025 * A275027 A275028 A275029

Keyword

nonn,more

Author

Jon E. Schoenfield, Nov 12 2016

Extensions

a(4)-a(5) from Max Alekseyev, Mar 21 2023

Status

approved