OFFSET
1,1
COMMENTS
Numbers n that have a unique representation as n = h^2 + i^2 + j^2 + k^2 with h,i,j,k odd and 0 < h < i < j < k.
No more terms up to 5*10^5. - Robert Israel, Jul 20 2018
a(13) > 5*10^6, if it exists. - Robert Price, Jul 25 2018
a(13) > 10^11, if it exists (which seems very unlikely). - Jon E. Schoenfield, Jul 28 2018
LINKS
Michael D. Hirschhorn, Partitions into Four Distinct Squares of Equal Parity, Australasian Journal of Combinatorics, Volume 24(2001), pp. 285-291.
Michael D. Hirschhorn, The Power of q: A Personal Journey, Springer 2017. See Chapter 31: Partitions into Four Distinct Squares of Equal Parity.
EXAMPLE
156 (a member of A316833) is not a member here since it has two representations: 156 = 1+25+49+81 = 1+9+25+121.
MAPLE
N:= 10000: # to get all terms <= N
V:= Vector(N):
for a from 1 to floor(sqrt(N/4)) by 2 do
for b from a+2 to floor(sqrt((N-a^2)/3)) by 2 do
for c from b+2 to floor(sqrt((N-a^2-b^2)/2)) by 2 do
for d from c + 2 by 2 do
r:= a^2+b^2+c^2+d^2;
if r > N then break fi;
V[r]:= V[r]+1
od od od od:
select(r -> V[r]=1, [$1..N]); # Robert Israel, Jul 20 2018
MATHEMATICA
okQ[n_] := Count[PowersRepresentations[n, 4, 2], pr_List /; Union[pr] == pr && AllTrue[pr, OddQ]] == 1;
Select[Range[1000], okQ] (* Jean-François Alcover, Apr 02 2019 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jul 19 2018
STATUS
approved