A348711 Integers sorted by decreasing value of sigma(x)/x^2, where sigma is the sum of divisors.

1, 2, 3, 4, 6, 5, 8, 12, 10, 7, 9, 14, 16, 18, 15, 20, 24, 11, 13, 30, 22, 21, 28, 36, 17, 26, 32, 40, 19, 27, 42, 48, 25, 34, 60, 23, 33, 44, 38, 54, 35, 45, 56, 72, 50, 39, 52, 29, 46, 31, 66, 84, 64, 70, 80, 90, 37, 51, 78, 96, 68, 58, 63, 120, 41, 62, 57, 76, 108, 55

Offset: 1

Author

Michel Marcus, Oct 31 2021

Keywords

• nonn

Comments

Is it possible to find distinct x and y such that sigma(x)/x^2 = sigma(y)/y^2 ?

Examples

			For 1,2,3,4,6,5,... sigma(x)/x^2 gives: 1 > 3/4 > 4/9 > 7/16 > 1/3 > 6/25 > ...
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Scatterplot of sigma(x)/x^2 for x=1..240, highlighting the position of superabundant x (in A004394) in red.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000203, A004394, A085790.

Programs

Mathematica

Block[{nn = Function[s, FirstPosition[s, #][[1]] &@ Fold[Max, s]]@ Array[DivisorSigma[1, #]/# &, 125], s}, s = Array[DivisorSigma[1, #]/#^2 &, nn]; #[[1 ;; FirstPosition[#, nn][[1]]]] &@ Map[FirstPosition[s, #][[1]] &, ReverseSort[s]]] (* Michael De Vlieger, Oct 31 2021 *)

PARI

lista(nn) = Vec(vecsort(vector(10*nn, k, -sigma(k)/k^2), , 1), nn);