%I A124978
%S A124978 1,4,18,34,50,66,82,114,90,130,150,178,162,198,318,210,250,234,322,406,
%T A124978 465,330,306,402,462,390,474,378,490,486,654,610,522,450,778,678,642,
%U A124978 570,666,726,594,714,770,774,986,630,738,945,1035,850,1222,978,1014,918
%N A124978 Smallest number which has exactly n different partitions as a sum of 
               4 squares x^2+y^2+z^2+t^2.
%C A124978 Is it known that a(n) always exists? - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Dec 18 2006
%H A124978 T. D. Noe, <a href="b124978.txt">Table of n, a(n) for n=1..1000</a>
%e A124978 a(4)=34 because 34 is smallest number which has 4 partitions 34=4^2+3^2+3^2+0^2 
               = 4^2+4^2+1^2+1^2 = 5^2+2^2+2^2+1^2 = 5^2+3^2+0^2+0^2
%e A124978 a(3)=18 which has 3 partitions 18=0^2+0^2+3^2+3^2=0^2+1^2+1^2+4^2=1^2+2^2+2^2+3^2.
%o A124978 (PARI) cnt4sqr(n)={ local(cnt=0,t2) ; for(x=0,floor(sqrt(n)), for(y=x,
               floor(sqrt(n-x^2)), for(z=y,floor(n-x^2-y^2), t2=n-x^2-y^2-z^2 ; 
               if( t2>=z^2 && issquare(n-x^2-y^2-z^2), cnt++ ; ) ; ) ; ) ; ) ; return(cnt) 
               ; } A124978(n)= { local(a=1) ; while(1, if( cnt4sqr(a)==n, return(a) 
               ; ) ; a++ ; ) ; } { for(n=1,100, print(n," ",A124978(n)) ; ) ; } 
               - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 29 2006
%Y A124978 Cf. A006431, A094942, A124979-A124983, A000378, A002635, A061262
%Y A124978 Sequence in context: A092116 A083969 A110621 this_sequence A031081 A009956 
               A031303
%Y A124978 Adjacent sequences: A124975 A124976 A124977 this_sequence A124979 A124980 
               A124981
%K A124978 nonn
%O A124978 1,2
%A A124978 Artur Jasinski (grafix(AT)csl.pl), Nov 14 2006
%E A124978 Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 29 2006
%E A124978 More terms from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Dec 18 2006