

A124978


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


4



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
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OFFSET

1,2


COMMENTS

Is it known that a(n) always exists?  Franklin T. AdamsWatters, 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}] (* JeanFrançois Alcover, Mar 11 2019 *)


PROG

(PARI) cnt4sqr(n)={ local(cnt=0, t2) ; for(x=0, floor(sqrt(n)), for(y=x, floor(sqrt(nx^2)), for(z=y, floor(nx^2y^2), t2=nx^2y^2z^2 ; if( t2>=z^2 && issquare(nx^2y^2z^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, A124979A124983, 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. AdamsWatters, Dec 18 2006


STATUS

approved



