A129246 - OEIS

%I #22 Jan 20 2025 16:23:15

%S 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,

%T 60,60,60,56,56,15,15,1,168,168,168,120,120,24,24,13,1,480,480,480,

%U 360,360,60,60,14,18,1,1512,1512,1512,1170,1170,168,168,24,39,12,1,4800,4800

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

%H Robert Israel, <a href="/A129246/b129246.txt">Table of n, a(n) for n = 1..10011</a> (first 142 antidiagonals, flattened)

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

%e Array begins:

%e k / sigma(...sigma(n)..) nested k deep.

%e 1.|.1...3...4....7....6....12....8....15...13....18...

%e 2.|.1...4...7....8...12....28...15....24...14....39...

%e 3.|.1...7...8...15...28....56...24....60...24....56...

%e 4.|.1...8..15...24...56...120...60...168...60...120...

%e 5.|.1..15..24...60..120...360..168...480..168...360...

%e 6.|.1..24..60..168..360..1170..480..1512..480..1170...

%e 7.|.1..60.168..480.1170..3276.1512..4800.1512..3276...

%e 8.|.1.168.480.1512.3276.10192.4800.15748.4800.10192...

%p 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

%t T[n_, k_] := T[n, k] = If[n == 1, DivisorSigma[1, k], DivisorSigma[1, T[n-1, k]]];

%t 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) *)

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

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

%K easy,nonn,tabl,look,changed

%O 1,3

%A _Jonathan Vos Post_, May 27 2007

%E More terms from _R. J. Mathar_, Oct 09 2007