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Numbers with relatively many and large divisors
From OeisWiki
The numbers with relatively many and large divisors are very interesting numbers to use as a base for the positional representation of numbers.
Definition
The number is in the sequence if and only if
where is the Euler-Mascheroni constant and sigma(n) is the sum of divisors of n.
This definition gives the sequence
A067698 Numbers with relatively many and large divisors (see comments).
- {2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 30, 36, 48, 60, 72, 84, 120, 180, 240, 360, 720, 840, 2520, 5040}
Robin has shown that 5040 is the last element in the sequence if and only if the Riemann hypothesis is true. Moreover the sequence is infinite if the Riemann hypothesis is false. Gronwall's theorem says that
See also
References
- Guy Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.