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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, 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
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
KEYWORD
nonn,more
AUTHOR
Jon E. Schoenfield, Nov 12 2016
EXTENSIONS
a(4)-a(5) from Max Alekseyev, Mar 21 2023
STATUS
approved