This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A225642 Irregular table read by rows: n-th row gives distinct values of successively iterated Landau-like functions for n, starting with the initial value n. 13
 1, 2, 3, 6, 4, 12, 5, 30, 60, 6, 30, 60, 7, 84, 420, 8, 120, 840, 9, 180, 1260, 2520, 10, 210, 840, 2520, 11, 330, 4620, 13860, 27720, 12, 420, 4620, 13860, 27720, 13, 780, 8580, 60060, 180180, 360360, 14, 630, 8190, 90090, 360360, 15, 840, 10920, 120120, 360360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The leftmost column of table (the initial term of each row, T(n,1)) is n, corresponding to lcm(n) computed from the singular {n} partition of n, after which, on the same row, each further term T(n,i) is computed by finding such a partition {p_1 + p_2 + ... + p_k} of n so that value of lcm(T(n, i-1), p_1, p_2, ..., p_k) 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). Of possible interest: which numbers occur only once in this table, and which occur multiple times? And how many times, if each number occurs only a finite number of times? Each number occurs a finite number of times: rows are increasing, first column is increasing, so n will occur last in row n, leftmost column. Primes (and other numbers too) occur once. - Alois P. Heinz, May 25 2013 LINKS Alois P. Heinz, Rows n = 1..150, flattened EXAMPLE The first fifteen rows of table are:    1;    2;    3,   6;    4,  12;    5,  30,    60;    6,  30,    60;    7,  84,   420;    8, 120,   840;    9, 180,  1260,   2520;   10, 210,   840,   2520;   11, 330,  4620,  13860,  27720;   12, 420,  4620,  13860,  27720;   13, 780,  8580,  60060, 180180, 360360;   14, 630,  8190,  90090, 360360;   15, 840, 10920, 120120, 360360; 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, t, lis}, t = b[n, n]; lis = {}; d = n; h = 0; While[d != h, AppendTo[lis, d]; h = d; d = Max[Table[LCM[h, i], {i, t}]]]; lis]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Mar 02 2016, after Alois P. Heinz *) PROG (Scheme with Antti Karttunen's IntSeq-library): (definec (A225642 n) (A225640bi (Aux_for_225642 n) (- n (A225645 (Aux_for_225642 n))))) ;; Scheme-definition of A225640bi given in A225640. (define Aux_for_225642 (COMPOSE -1+ (LEAST-GTE-I 1 1 A225645) 1+)) ;; Auxiliary function not submitted separately, which gives the row-number for the n-th term. ;; It starts as 1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, ... CROSSREFS Cf. A225644 (length of n-th row), A225646 (for n >= 3, second term of n-th row). Cf. A003418 (largest and rightmost term of n-th row). Cf. A225640, A225641, A225645. Cf. A225632 (each row starts with 1 instead of n). Cf. A226055 (the first common term with A225632 on the n-th row). Cf. A225639 (distance to that first common term). Cf. A226056 (number of trailing common terms with A225632 on the n-th row). Sequence in context: A305325 A302848 A046202 * A273317 A122866 A097275 Adjacent sequences:  A225639 A225640 A225641 * A225643 A225644 A225645 KEYWORD nonn,tabf AUTHOR Antti Karttunen, May 15 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 15:24 EDT 2019. Contains 323572 sequences. (Running on oeis4.)