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%I #27 Mar 13 2018 04:10:42
%S 1,1,2,1,3,6,1,4,12,1,6,30,60,1,6,30,60,1,12,84,420,1,15,120,840,1,20,
%T 180,1260,2520,1,30,210,840,2520,1,30,420,4620,13860,27720,1,60,660,
%U 4620,13860,27720,1,60,780,8580,60060,180180,360360
%N Irregular table read by rows: n-th row gives distinct values of successively iterated Landau-like functions for n, starting with the initial value 1.
%C The leftmost column of table (the initial term of each row, T(n,1)) is 1, corresponding to lcm(1,1,...,1) computed from the {1+1+...+1} partition of n, after which, on the same row, each further term T(n,i) is computed by finding such a partition [p1,p2,...,pk] of n so that value of lcm(T(n,i-1), p1,p2,...,pk) is maximized, until finally A003418(n) is reached, which will be listed as the last term of row n (as the result would not change after that, if we continued the same process).
%H Alois P. Heinz, <a href="/A225632/b225632.txt">Rows n = 1..150, flattened</a>
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%e The first fifteen rows of table are:
%e 1;
%e 1, 2;
%e 1, 3, 6;
%e 1, 4, 12;
%e 1, 6, 30, 60;
%e 1, 6, 30, 60;
%e 1, 12, 84, 420;
%e 1, 15, 120, 840;
%e 1, 20, 180, 1260, 2520;
%e 1, 30, 210, 840, 2520;
%e 1, 30, 420, 4620, 13860, 27720;
%e 1, 60, 660, 4620, 13860, 27720;
%e 1, 60, 780, 8580, 60060, 180180, 360360;
%e 1, 84, 1260, 16380, 180180, 360360;
%e 1, 105, 4620, 60060, 180180, 360360;
%p b:= proc(n, i) option remember; `if`(n=0, {1},
%p `if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),
%p b(n-i*j, i-1))[], j=0..n/i)}))
%p end:
%p T:= proc(n) option remember; local d, h, l, ll;
%p l:= b(n$2); ll:= NULL; d:=1; h:=0;
%p while d<>h do ll:= ll, d; h:= d;
%p d:= max(seq(ilcm(h, i), i=l))
%p od; ll
%p end:
%p seq(T(n), n=1..20); # _Alois P. Heinz_, May 29 2013
%t b[n_, i_] := b[n, i] = If[n==0, {1}, If[i<1, {}, Table[Map[Function[{x}, LCM[x, If[j==0, 1, i]]], b[n-i*j, i-1]], {j, 0, n/i}]]]; T[n_] := T[n] = Module[{d, h, l, ll}, l=b[n, n]; ll={}; d=1; h=0; While[d != h, AppendTo[ll, d]; h=d; d = Max[ Table[LCM[h, i], {i, l}]]]; ll]; Table[T[n], {n, 1, 20}] // Flatten (* _Jean-François Alcover_, Jul 29 2015, after _Alois P. Heinz_ *)
%o (Scheme with _Antti Karttunen_'s IntSeq-library):
%o (definec (A225632 n) (A225630bi (Aux_for_225632 n) (- n (A225635 (Aux_for_225632 n))))) ;; Scheme-definition for A225630bi given in A225630.
%o (define Aux_for_225632 (COMPOSE -1+ (LEAST-GTE-I 1 1 A225635) 1+)) ;; Auxiliary function not submitted separately, which gives the row-number for the n-th term.
%o ;; It starts as 1,2,2,3,3,3,4,4,4,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,9,...
%Y Cf. A225634 (length of n-th row), A000793 (n>=2 gives the second column).
%Y Cf. A225629 (second largest/rightmost term of n-th row).
%Y Cf. A003418 (largest/rightmost term of n-th row).
%Y Cf. A225630, A225631, A225635, A212721.
%Y Cf. A225642 (row n starts from n instead of 1).
%Y Cf. A226055 (the first term common with A225642 on the n-th row).
%Y Cf. A225638 (distance to that first common term from the beginning of the row n).
%Y Cf. A226056 (number of trailing terms common with A225642 on the n-th row).
%K nonn,tabf
%O 1,3
%A _Antti Karttunen_, May 13 2013
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