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A081454
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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.
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4
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| In case there is more than one solution, choose the one where the maximal number is minimal.
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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.
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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 (mathar(AT)strw.leidenuniv.nl), Nov 12 2006
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CROSSREFS
| Cf. A081455, A081456, A081457.
Sequence in context: A084460 A120578 A096249 * A133883 A004160 A128077
Adjacent sequences: A081451 A081452 A081453 * A081455 A081456 A081457
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KEYWORD
| tabl,nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 21 2003
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EXTENSIONS
| Edited and extended by David Garber (garber(AT)math.huji.ac.il), Jun 17 2003
More terms from Ray G. Opao (1260(AT)email.com), Aug 01 2005
Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 12 2006
More terms from Max Alekseyev (maxale(AT)gmail.com), Apr 25 2009
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