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a(n) is the least primitive n-abundant number k with the largest possible abundancy index sigma(k)/k.
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%I #11 Apr 29 2019 20:57:48

%S 3465,6930,19399380,8172244080

%N a(n) is the least primitive n-abundant number k with the largest possible abundancy index sigma(k)/k.

%C 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.

%C 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.

%H Graeme L. Cohen, <a href="https://doi.org/10.1090/S0025-5718-1984-0744936-X ">Primitive alpha-abundant numbers</a>, Mathematics of Computation, Vol. 43, No. 167 (1984), pp. 263-270.

%e 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...

%Y Cf. A000203, A071395, A307112, A307114, A307115.

%K nonn,hard,bref,more

%O 2,1

%A _Amiram Eldar_, Mar 25 2019