A333053 -id:A333053 - cp's OEIS frontend

A333054 Numbers m such that r(m) > r(k) for all k < m, where r(m) = min(sigma(m)/m, sigma(m+1)/(m+1)), and sigma(m) is the sum of divisors of m (A000203).

1, 2, 8, 14, 44, 104, 495, 944, 4095, 5775, 5984, 21735, 98175, 862784, 4096575, 7194824, 14753024, 879207615, 1969789184, 2275962975, 3968862975, 12567844575, 39566665215, 44803620225, 77510285775, 125617830975, 162902829375

Offset: 1

Amiram Eldar, Mar 06 2020

The corresponding values of r(a(n)) are 1, 1.333..., 1.444..., 1.6, 1.733..., 1.828..., 1.890..., 1.970..., 1.999..., 2.044..., 2.085..., 2.120..., 2.181..., 2.243..., 2.248..., 2.252..., 2.360..., 2.397..., 2.407..., 2.408..., 2.411...
The least number m such that both m and m+1 are k-abundant (i.e., their abundancy indices sigma(m)/m > k and sigma(m+1)/(m+1) > k) is a term in this sequence. E.g., a(10) = 5775 = A096399(1).
a(28) > 5*10^11. - Amiram Eldar, Jan 02 2021

			The values of min(sigma(k)/k, sigma(k+1)/(k+1)) for k = 1, 2, ... 8 are 1, 4/3, 4/3, 6/5, 6/5, 8/7, 8/7, 13/9. The record values in this range, 1, 4/3 and 13/9, are obtained at k = 1, 2, and 8.

Cf. A000203, A004394, A068403, A096399, A333053.

seq={}; rminmax = 0; r1 = 1; Do[r2 = DivisorSigma[1, n]/n; rmin = Min[r1, r2]; If[rmin > rminmax, rminmax = rmin; AppendTo[seq, n-1]]; r1 = r2, {n, 2, 10^6}]; seq

a(22)-a(27) from Amiram Eldar, Jan 02 2021

cp's OEIS Frontend

A333054 Numbers m such that r(m) > r(k) for all k < m, where r(m) = min(sigma(m)/m, sigma(m+1)/(m+1)), and sigma(m) is the sum of divisors of m (A000203).

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