OFFSET
1,3
COMMENTS
In case there is more than one solution, choose the one where the maximal number is minimal.
LINKS
Max Alekseyev, Rows n = 1..50, flattened
EXAMPLE
Triangle begins:
1;
1, 4;
1, 2, 8;
1, 2, 3, 6;
1, 2, 3, 4, 6;
1, 2, 3, 4, 6, 9;
1, 2, 3, 5, 6, 8, 10;
1, 2, 3, 4, 5, 6, 8, 10;
1, 2, 3, 4, 5, 6, 8, 9, 10;
...
The 7th row could also be 1, 2, 3, 4, 5, 8, 15, but this has a larger last term.
MAPLE
A081454aux := proc(n, s, mfact) local d, findx, f ; if n = 1 then if s <= mfact then RETURN([s]) ; else RETURN([]) ; fi ; else d := numtheory[divisors](s) ; for findx from n to nops(d) do if op(findx, d) <= mfact then f := A081454aux(n-1, s/op(findx, d), op(findx, d)-1) ; if nops(f) <> 0 then RETURN([op(f), op(findx, d)]) ; fi ; fi ; od ; RETURN([]) ; fi ; end: A081454row := proc(n) local p, s, d, findx, f ; p :=1 ; s :=1 ; while true do d := numtheory[divisors](s) ; if nops(d) >= n then if n = 1 then RETURN([1]) ; else for findx from n to nops(d) do f := A081454aux(n-1, s/op(findx, d), op(findx, d)-1) ; if nops(f) <> 0 then RETURN([op(f), op(findx, d)]) ; fi ; od; fi ; fi ; p := p+1 ; s := p^2 ; od ; end: for n from 1 to 14 do r := A081454row(n) : for i from 1 to n do printf("%d, ", op(i, r) ) ; od ; od : # R. J. Mathar, Nov 12 2006
MATHEMATICA
T[n_] := T[n] = SortBy[MinimalBy[Select[Subsets[Range[2n+2], {n}], #[[1]] == 1 && IntegerQ@Sqrt[Times @@ #]&], Times @@ #&], Last] // First;
Table[Print[n, " ", T[n]]; T[n], {n, 1, 12}] // Flatten (* Jean-François Alcover, Jun 03 2023 *)
CROSSREFS
KEYWORD
tabl,nonn
AUTHOR
Amarnath Murthy, Mar 21 2003
EXTENSIONS
Edited and extended by David Garber, Jun 17 2003
More terms from Ray G. Opao, Aug 01 2005
Corrected and extended by R. J. Mathar, Nov 12 2006
More terms from Max Alekseyev, Apr 25 2009
Correct row #13 conjectured by Jean-François Alcover and confirmed by Max Alekseyev, Jun 03 2023
STATUS
approved