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A161882 Smallest k such that n^2 = a_1^2 + ... + a_k^2 and all a_i are positive integers less than n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
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
LINKS
Eric Weisstein's World of Mathematics, Diophantine Equation 2nd Powers.
FORMULA
a(n)=2 iff n is in A009003 (hypotenuse numbers), a(n)=4 iff n is in A000079 (powers of 2), otherwise a(n)=3. - M. F. Hasler, Dec 17 2014
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A215597 A266110 A204819 * A276789 A082125 A058290
KEYWORD
nonn
AUTHOR
Dmitry Kamenetsky, Jun 21 2009
EXTENSIONS
More terms from Alois P. Heinz, Dec 04 2014
STATUS
approved

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Last modified April 21 10:04 EDT 2024. Contains 371852 sequences. (Running on oeis4.)