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
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
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, May 13 2013
STATUS
approved