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A161882
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Smallest k such that n^2 = a_1^2+...+a_k^2 and all a_i are positive integers less than n.
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6
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4, 3, 4, 2, 3, 3, 4, 3, 2, 3, 3, 2, 3, 2, 4, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 2, 2, 3, 4, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 4, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2
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OFFSET
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2,1
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COMMENTS
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Related to hypotenuse numbers: A161882(A009003(n))=2 for all n.
Jacobi's four-square theorem can be used to show that a(n) <= 4. - Charles R Greathouse IV, Jul 31 2011
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 2..700
Jean-Charles Meyrignac, Computing minimal equal sums of like powers
Weisstein, Eric W., Diophantine Equation 2nd Powers
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FORMULA
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a(n)=2 iff n is in A009003 (hypotenuse numbers) , a(n)=4 iff n is in A000079 (powers of 2), else a(n)=3. - M. F. Hasler, Dec 17 2014
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EXAMPLE
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2^2 = 1^2 + 1^2 + 1^2 + 1^2, so a(2)=4. 3^2 = 2^2 + 2^2 + 1^2, so a(3)=3.
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MATHEMATICA
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f[n_, k_] := Select[PowersRepresentations[n^2, k, 2], AllTrue[#, 0<#<n&]&];
a[n_] := For[k = 2, True, k++, If[f[n, k] != {}, Return[k]]];
a /@ Range[2, 200] (* Jean-François Alcover, Oct 03 2020 *)
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PROG
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(PARI) A161882(n)={vecmin(factor(n)[, 1]%4)==1 && return(2); if(n==1<<valuation(n, 2), 4, 3)} \\ M. F. Hasler, Dec 17 2014
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CROSSREFS
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Cf. A161883, A161884, A161885.
Sequence in context: A215597 A266110 A204819 * A276789 A082125 A058290
Adjacent sequences: A161879 A161880 A161881 * A161883 A161884 A161885
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KEYWORD
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nonn
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AUTHOR
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Dmitry Kamenetsky, Jun 21 2009
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EXTENSIONS
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More terms from Alois P. Heinz, Dec 04 2014
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STATUS
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approved
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