A318083 Numbers m such that sigma(sigma(m))/sigma(m) <= sigma(m)/m.

1, 2, 4, 8, 9, 12, 16, 18, 25, 32, 36, 48, 50, 52, 64, 72, 80, 81, 84, 90, 98, 100, 108, 112, 128, 144, 150, 156, 162, 180, 192, 196, 200, 208, 225, 240, 242, 244, 252, 256, 288, 289, 292, 300, 320, 324, 336, 338, 360, 372, 388, 392, 400, 420, 432, 441, 444, 448, 450, 468, 484

Offset: 1

Author

Michel Marcus, Aug 15 2018

Keywords

• nonn

Comments

A318059 and A318060 give f(n) = sigma(sigma(n))/n.

Let g(n) = sigma(n)/n, then f(n) = g(sigma(n))*g(n).

For g(), see A017665 and A017666.

Then this sequence are the integers m for which g(sigma(m)) <= g(m).

Are there other integers than 1, for which sigma(sigma(m))/sigma(m) = sigma(m)/m?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203 (sigma), A017665, A017666, A051027, A318059, A318060, A318084.

Programs

Mathematica

q[n_] := Module[{s = DivisorSigma[1, n]}, DivisorSigma[1, s]/s <= s/n]; Select[Range[500], q] (* Amiram Eldar, Apr 04 2024 *)

PARI

isok(n) = my(sn=sigma(n)); sigma(sn)/sn <= sn/n;