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

1,3

Links

Table of n, a(n) for n=1..69.

Formula

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

Example

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...

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) *)

Crossrefs

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

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

Sequence in context: A246340 A246354 A286625 * A125608 A182001 A099813

Adjacent sequences: A129243 A129244 A129245 * A129247 A129248 A129249

Keyword

easy,nonn,tabl

Author

Jonathan Vos Post, May 27 2007

Extensions

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

Status

approved