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 A081454 Triangle read by rows in which the n-th row contains n distinct numbers such that their product is a square, which is minimal over all choices for n distinct numbers. 4
 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, 1, 2, 3, 4, 5, 6, 7, 9, 10, 14, 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 15, 16, 1, 2, 3, 4, 6, 7, 8, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS In case there is more than one solution, choose the one where the maximal number is minimal. LINKS 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 CROSSREFS Cf. A081455, A081456, A081457. Sequence in context: A216863 A120578 A096249 * A133883 A279816 A004160 Adjacent sequences:  A081451 A081452 A081453 * A081455 A081456 A081457 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 STATUS approved

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Last modified September 26 12:04 EDT 2021. Contains 347665 sequences. (Running on oeis4.)