OFFSET
2,1
COMMENTS
A primitive n-abundant number k is a number with sigma(k)/k > n and sigma(d)/d < n for all the proper divisors d of k.
Cohen proved that for any given eps > 0 there are only finitely many primitive n-abundant numbers k with sigma(k)/k >= n + eps. Thus for each n there is a maximal value of the abundancy index sigma(k)/k for primitive n-abundant numbers k. If this maximum occurs at more than one number the least of them is given in this sequence.
LINKS
Graeme L. Cohen, Primitive alpha-abundant numbers, Mathematics of Computation, Vol. 43, No. 167 (1984), pp. 263-270.
EXAMPLE
3465 is in the sequence since it is the primitive abundant (A071395) number with the largest possible abundancy index among the primitive abundant numbers: sigma(3465)/3465 = 832/385 = 2.161003... The abundancy indices of the next terms are 1248/385 = 3.241558..., 193536/46189 = 4.190088..., 642816/124729 = 5.153701...
CROSSREFS
KEYWORD
nonn,hard,bref,more
AUTHOR
Amiram Eldar, Mar 25 2019
STATUS
approved