A353615 a(n) is the numerator of the median abundancy index of the first 2^n + 1 positive integers.

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

Author

Amiram Eldar, Apr 30 2022

Keywords

• nonn
• frac
• more

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).

Examples

			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.
		

Crossrefs

Cf. A000203, A017665, A017666, A353616 (denominators), A353617.

Programs

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}]]

Formula

Limit_{n->oo} a(n)/A353616(n) = A353617.