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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. 0
1, 24, 122522400 (list; graph; refs; listen; history; text; internal format)
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)

LINKS

Table of n, a(n) for n=1..3.

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,bref,more

AUTHOR

Jon E. Schoenfield, Nov 12 2016

STATUS

approved

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Last modified August 2 16:58 EDT 2021. Contains 346428 sequences. (Running on oeis4.)