|
| |
|
|
A129246
|
|
Iterated sum of divisors array A[k,n] = k-th iterate of sigma(n), by antidiagonals.
|
|
6
|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
KEYWORD
|
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
