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A353615
a(n) is the numerator of the median abundancy index of the first 2^n + 1 positive integers.
2
4, 4, 13, 3, 32, 45, 63, 90, 111, 162, 210, 237, 7502, 11776, 240, 2944, 3008, 11648, 225152, 478080, 2704000, 1548160, 2462400, 10128256, 4999296, 8640768, 48264064, 32347648
OFFSET
1,1
COMMENTS
The abundancy index of a number k is sigma(k)/k = A017665(k)/A017666(k), where sigma is the sum-of-divisors function (A000203).
FORMULA
Limit_{n->oo} a(n)/A353616(n) = A353617.
EXAMPLE
The fractions begin with 4/3, 4/3, 13/9, 3/2, 32/21, 45/29, 63/41, 90/59, 111/73, 162/107, ...
The abundancy indices of the first 3 positive integers are 1, 3/2 and 4/3. The median is a(1)/A353616(1) = 4/3.
MATHEMATICA
With[{m = 20}, t = Table[DivisorSigma[-1, n], {n, 1, 2^m + 1}]; Numerator @ Table[Median[t[[1 ;; 2^n + 1]]], {n, 1, m}]]
CROSSREFS
Cf. A000203, A017665, A017666, A353616 (denominators), A353617.
Sequence in context: A228612 A038804 A183362 * A088838 A367688 A127403
KEYWORD
nonn,frac,more
AUTHOR
Amiram Eldar, Apr 30 2022
STATUS
approved