A090896 a(n) = sigma^n(n), where sigma^n denotes functional iteration.

1, 4, 8, 24, 120, 1170, 1512, 15748, 15748, 61440, 196584, 1572840, 1098240, 15605760, 50328576, 7074432, 355532800, 2143289344, 13815410400, 224319234048, 33541980160, 109760857440, 1468475386560, 33151875434496, 1415960985600, 1510712608204800

Offset: 1

Author

Gabriel Cunningham (gcasey(AT)mit.edu), Feb 25 2004

Keywords

• nonn

Comments

a(8) = a(9). Are there any other numbers m, n such that a(m) = a(n)? a(16) < a(15); a(25) < a(24). How often is a(n+1) < a(n)?

a(88) = a(89), a(108) = a(109) and a(124) = a(125). - Seiichi Manyama, May 08 2021

Examples

			a(3) = sigma^3(3) = sigma^2(4) = sigma(7) = 8
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200

Crossrefs

Main diagonal of A129246.

Cf. A000203, A101303.

Programs

Maple

a:= n-> (numtheory[sigma]@@n)(n):
seq(a(n), n=1..30);  # Alois P. Heinz, Oct 03 2018

Mathematica

a[n_] := Nest[DivisorSigma[1, #]&, n, n];
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jan 30 2025 *)

PARI

a(n) = my(k=sigma(n)); for(n=2, n, k=sigma(k)); k; \\ Seiichi Manyama, May 08 2021