

A083486


Triangle read by rows in which the nth row contains the smallest set of n distinct numbers beginning with n with a product which is a square.


3



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
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OFFSET

1,2


COMMENTS

Presumably "smallest set" means we start with n1 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 n1 numbers by reducing all prime exponents modulo 2. If the result is <= the (n1)st term, multiply by j^2, j=2,3,4,.. until it is.  R. J. Mathar, Apr 05 2007


LINKS

Table of n, a(n) for n=1..72.


EXAMPLE

1
2 8
3 4 12
4 5 6 30
5 6 7 8 105
...


MAPLE

A083486 := proc(n, m) local fs, k, resu, extr ; if m < n then n+m1; else fs := ifactors(mul( A083486(n, k), k=1..n1))[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, n1) 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, Apr 05 2007


CROSSREFS

Cf. A083484, A083485.
Sequence in context: A214072 A016640 A321984 * A076031 A076596 A081967
Adjacent sequences: A083483 A083484 A083485 * A083487 A083488 A083489


KEYWORD

nonn,tabl


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003


EXTENSIONS

Corrected and extended by R. J. Mathar, Apr 05 2007
Example corrected by Harvey P. Dale, Aug 05 2021


STATUS

approved



