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Search: id:A083486
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| A083486 |
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Triangle read by rows in which the n-th row contains the smallest set of n distinct numbers beginning with n with a product which is a square. |
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+0
3
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| 1, 2, 8, 3, 4, 12, 4, 5, 6, 30, 5, 6, 7, 8, 105, 6, 7, 8, 9, 10, 210, 7, 8, 9, 10, 11, 12, 1155, 8, 9, 10, 11, 12, 13, 14, 30030, 9, 10, 11, 12, 13, 14, 15, 16, 1001, 10, 11, 12, 13, 14, 15, 16, 17, 18, 34034, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 323323, 12, 13, 14, 15, 16, 17
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Presumably "smallest set" means we start with n-1 consecutive numbers in each row and add the last element to satisfy the requirement on the square, the last element is obtained from the prime factorization of the product of the first n-1 numbers by reducing all prime exponents modulo 2. If the result is <= the (n-1)-st term, multiply by j^2, j=2,3,4,.. until it is. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 05 2007
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EXAMPLE
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1
2 8
3 4 27
4 5 6 30
5 6 7 8 105
...
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MAPLE
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A083486 := proc(n, m) local fs, k, resu, extr ; if m < n then n+m-1; else fs := ifactors(mul( A083486(n, k), k=1..n-1))[2] ; resu := mul( op(1, op(k, fs))^(op(2, op(k, fs)) mod 2), k=1..nops(fs)) ; extr := 1 ; while extr^2*resu <= A083486(n, n-1) do extr := extr+1 ; od ; RETURN(resu*extr^2) ; fi ; end: for n from 1 to 15 do for m from 1 to n do printf("%a ", A083486(n, m)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 05 2007
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CROSSREFS
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Cf. A083484, A083485.
Sequence in context: A006085 A021357 A016640 this_sequence A076031 A076596 A081967
Adjacent sequences: A083483 A083484 A083485 this_sequence A083487 A083488 A083489
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KEYWORD
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nonn,tabl
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (amarnath_murthy(AT)yahoo.com), May 03 2003
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 05 2007
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