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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified May 14 06:28 EDT 2021. Contains 343879 sequences. (Running on oeis4.)