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

1,2

Comments

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

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A004394, A085790.

Sequence in context: A032447 A224531 A058213 * A080997 A151942 A054582

Adjacent sequences: A348708 A348709 A348710 * A348712 A348713 A348714

Keyword

nonn

Author

Michel Marcus, Oct 31 2021

Status

approved