A129246 Iterated sum of divisors array A[k,n] = k-th iterate of sigma(n), by upward antidiagonals.

1, 1, 3, 1, 4, 4, 1, 7, 7, 7, 1, 8, 8, 8, 6, 1, 15, 15, 15, 12, 12, 1, 24, 24, 24, 28, 28, 8, 1, 60, 60, 60, 56, 56, 15, 15, 1, 168, 168, 168, 120, 120, 24, 24, 13, 1, 480, 480, 480, 360, 360, 60, 60, 14, 18, 1, 1512, 1512, 1512, 1170, 1170, 168, 168, 24, 39, 12, 1, 4800, 4800

Offset: 1

Author

Jonathan Vos Post, May 27 2007

Keywords

• easy
• nonn
• tabl
• look

Examples

			Array begins:
k / sigma(...sigma(n)..) nested k deep.
1.|.1...3...4....7....6....12....8....15...13....18...
2.|.1...4...7....8...12....28...15....24...14....39...
3.|.1...7...8...15...28....56...24....60...24....56...
4.|.1...8..15...24...56...120...60...168...60...120...
5.|.1..15..24...60..120...360..168...480..168...360...
6.|.1..24..60..168..360..1170..480..1512..480..1170...
7.|.1..60.168..480.1170..3276.1512..4800.1512..3276...
8.|.1.168.480.1512.3276.10192.4800.15748.4800.10192...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (first 142 antidiagonals, flattened)

Crossrefs

Cf. A000203 (row 1), A051027 (row 2), A066971 (row 3).

Cf. A000012 (column 1), A007497 (column 2), A090896 (main diagonal).

Programs

Maple

A129246 := proc(k,n) option remember ; if k= 1 then numtheory[sigma](n); else A129246(k-1,numtheory[sigma](n)) ; fi ; end: for d from 1 to 13 do for n from 1 to d do printf("%d, ",A129246(d+1-n,n)) ; od: od: # R. J. Mathar, Oct 09 2007

Mathematica

T[n_, k_] := T[n, k] = If[n == 1, DivisorSigma[1, k], DivisorSigma[1, T[n-1, k]]];
Table[T[d-k+1, k], {d, 1, 13}, {k, 1, d}] // Flatten (* Jean-François Alcover, Sep 23 2022, after R. J. Mathar, except that T(n,k) replaces the unusual A(k,n) *)

Formula

A[k,n] = sigma^k(n), where sigma^k denotes functional iteration.

Extensions

More terms from R. J. Mathar, Oct 09 2007