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 A225632 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. 14
 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, 180, 1260, 2520, 1, 30, 210, 840, 2520, 1, 30, 420, 4620, 13860, 27720, 1, 60, 660, 4620, 13860, 27720, 1, 60, 780, 8580, 60060, 180180, 360360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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). LINKS Alois P. Heinz, Rows n = 1..150, flattened EXAMPLE The first fifteen rows of table are:   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,  180,  1260,   2520;   1,  30,  210,   840,   2520;   1,  30,  420,  4620,  13860,  27720;   1,  60,  660,  4620,  13860,  27720;   1,  60,  780,  8580,  60060, 180180, 360360;   1,  84, 1260, 16380, 180180, 360360;   1, 105, 4620, 60060, 180180, 360360; MAPLE b:= proc(n, i) option remember; `if`(n=0, {1},       `if`(i<1, {}, {seq(map(x->ilcm(x, `if`(j=0, 1, i)),        b(n-i*j, i-1))[], j=0..n/i)}))     end: T:= proc(n) option remember; local d, h, l, ll;       l:= b(n\$2); ll:= NULL; d:=1; h:=0;       while d<>h do ll:= ll, d; h:= d;         d:= max(seq(ilcm(h, i), i=l))       od; ll     end: seq(T(n), n=1..20);  # Alois P. Heinz, May 29 2013 MATHEMATICA 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 *) PROG (Scheme with Antti Karttunen's IntSeq-library): (definec (A225632 n) (A225630bi (Aux_for_225632 n) (- n (A225635 (Aux_for_225632 n))))) ;; Scheme-definition for A225630bi given in A225630. (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. ;; 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, ... CROSSREFS Cf. A225634 (length of n-th row), A000793 (n>=2 gives the second column). Cf. A225629 (second largest/rightmost term of n-th row). Cf. A003418 (largest/rightmost term of n-th row). Cf. A225630, A225631, A225635, A212721. Cf. A225642 (row n starts from n instead of 1). Cf. A226055 (the first term common with A225642 on the n-th row). Cf. A225638 (distance to that first common term from the beginning of the row n). Cf. A226056 (number of trailing terms common with A225642 on the n-th row). Sequence in context: A078760 A103280 A046899 * A035206 A210238 A209936 Adjacent sequences:  A225629 A225630 A225631 * A225633 A225634 A225635 KEYWORD nonn,tabf AUTHOR Antti Karttunen, May 13 2013 STATUS approved

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Last modified May 22 20:59 EDT 2019. Contains 323486 sequences. (Running on oeis4.)