A124978 Smallest number which has exactly n different partitions as a sum of 4 squares x^2+y^2+z^2+t^2.

1, 4, 18, 34, 50, 66, 82, 114, 90, 130, 150, 178, 162, 198, 318, 210, 250, 234, 322, 406, 465, 330, 306, 402, 462, 390, 474, 378, 490, 486, 654, 610, 522, 450, 778, 678, 642, 570, 666, 726, 594, 714, 770, 774, 986, 630, 738, 945, 1035, 850, 1222, 978, 1014, 918

Offset

1,2

Comments

Is it known that a(n) always exists? - Franklin T. Adams-Watters, Dec 18 2006

A002635(a(n)) = n. - Reinhard Zumkeller, Jul 13 2014

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Index entries for sequences related to sums of squares

Example

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
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.

Mathematica

kmin[n_] := If[n<5, 1, 10n](* empirical, should be lowered in case of doubt *);
a[n_] := a[n] = For[k=kmin[n], True, k++, If[Length[PowersRepresentations[ k, 4, 2]] == n, Return[k]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 1000}] (* Jean-François Alcover, Mar 11 2019 *)

Prog

(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, Nov 29 2006
(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a124978 = (+ 1) . fromJust . (`elemIndex` (tail a002635_list))
-- Reinhard Zumkeller, Jul 13 2014

Crossrefs

Cf. A006431, A094942, A124979-A124983, A000378, A002635, A061262.

Sequence in context: A092116 A083969 A110621 * A031081 A009956 A031303

Adjacent sequences: A124975 A124976 A124977 * A124979 A124980 A124981

Keyword

nonn

Author

Artur Jasinski, Nov 14 2006

Extensions

Corrected and extended by R. J. Mathar, Nov 29 2006

More terms from Franklin T. Adams-Watters, Dec 18 2006

Status

approved