OFFSET
1,2
COMMENTS
Conjecture: a(448) does not exist, i.e., there is no number with exactly 448 such representations. - Robert Israel, Nov 15 2017
REFERENCES
E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, New York, 1985, p. 86, Theorem 1.
LINKS
Robert Israel, Table of n, a(n) for n = 1..447 (first 200 terms from Robert Price)
D. H. Lehmer, On the Partition of Numbers into Squares, The American Mathematical Monthly, Vol. 55, No. 8, October 1948, pp. 476-481.
FORMULA
A000174(a(n))=n. - Robert Israel, Nov 15 2017
MAPLE
N:= 1000: # to get a(1)...a(n) where a(n+1) is the first term > N
V:= Array(0..N):
for x[1] from 0 to floor(sqrt(N/5)) do
for x[2] from x[1] while x[1]^2 + 4*x[2]^2 <= N do
for x[3] from x[2] while x[1]^2 + x[2]^2 + 3*x[3]^2 <= N do
for x[4] from x[3] while x[1]^2 + x[2]^2 + x[3]^2 + 2*x[4]^2 <= N do
for x[5] from x[4] while x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2 + x[5]^2 <= N do
t:= x[1]^2 + x[2]^2 + x[3]^2 + x[4]^2 + x[5]^2;
V[t]:= V[t]+1;
od od od od od:
A:= Vector(max(V), -1):
for i from 0 to N do if A[V[i]]=-1 then A[V[i]]:= i fi od:
T:= select(t -> A[t]=-1, [$1..max(V)]):
if T = [] then nmax:= max(V) else nmax:= T[1]-1 fi:
convert(A[1..nmax], list); # Robert Israel, Nov 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Price, Nov 15 2017
STATUS
approved