

A295159


Smallest number with exactly n representations as a sum of five nonnegative squares.


3



0, 4, 13, 20, 29, 37, 50, 52, 61, 74, 77, 85, 91, 101, 106, 118, 125, 131, 133, 139, 162, 157, 154, 166, 178, 194, 187, 205, 203, 202, 227, 211, 226, 235, 234, 269, 251, 275, 250, 266, 291, 274, 259, 283, 301, 325, 306, 298, 326, 334, 347, 322, 362, 447, 331
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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. SpringerVerlag, 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. 476481.


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

Cf. A000174, A006431, A294675.
Sequence in context: A299182 A030744 A173512 * A298216 A299092 A299874
Adjacent sequences: A295156 A295157 A295158 * A295160 A295161 A295162


KEYWORD

nonn


AUTHOR

Robert Price, Nov 15 2017


STATUS

approved



