Search: id:A052261
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%I A052261
%S A052261 1,50,54,52,53,54,55,56,57,61,67,66,67,68,74,0,79,83,87,83,84,88,0,93,
%T A052261 96,105,101,110,106,102,116,0,108,0,0,0,117,0,117,121,0,125,0,135,0,0,
               0,
%U A052261 134,0,137,145,144,143,0,0,156,0,0,152,0,0,157,0,0,0,169,0,166,0,166,0
%N A052261 Smallest integer that can be expressed as the sum of n squares of positive 
               integers in exactly n distinct ways, or 0 if no such number exists.
%C A052261 If the number of ways to write m as the sum of n squares is at least 
               x for m in the range k^2 to 2k^2+2k+1, it is at least x for any larger 
               m; take the smallest square j^2 greater than x/2 and x-j^2 >= m^2 
               has at least x representations, none of which obviously can exceed 
               j^2. The 0's for n=16 and 23 can be verified in this way with k=10; 
               32 to 35 with k=11; 36 with k=12; 38 to 49 with k=13; and 54 up with 
               k=14. For n sufficiently large, a(n) = (index of n in A111178) + 
               n, or 0 if n does not occur in A111178. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Jul 15 2006
%H A052261 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%e A052261 a_2 = 50 = 1^2 + 7^2 = 5^2 +5^2
%o A052261 (PARI) numsumsq(n, m) = local(p, i); p=1+x*O(x^m)+y*O(y^n);for(i=1,sqrtint(m),
               p=p/(1-x^i^2*y));p=polcoeff(p,n,y);vector(m,i,polcoeff(p,i)) vecfind(v, 
               x) = local(i, y); for(i=1,matsize(v)[2],if(v[i]==x,y=i;break()));
               y a(n, m=1000) = v=numsumsq(n,m);vecfind(v,n) /* values must be checked 
               */ - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 15 2006
%Y A052261 Cf. A111178.
%Y A052261 Sequence in context: A134691 A139182 A081646 this_sequence A118146 A114504 
               A046832
%Y A052261 Adjacent sequences: A052258 A052259 A052260 this_sequence A052262 A052263 
               A052264
%K A052261 nonn,nice
%O A052261 1,2
%A A052261 David M. Grumm (dmg(AT)head-cfa.harvard.edu), Feb 03 2000
%E A052261 a_16 > 119; values for a_17 through a_22 are 79, 83, 87, 83, 84, 88
%E A052261 a_16 > 10000, a_23 > 10000, if they exist. - Naohiro Nomoto (6284968128(AT)geocities.co.jp), 
               Aug 22 2001
%E A052261 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 15 
               2006

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