

A025358


Numbers that are the sum of 4 nonzero squares in exactly 2 ways.


1



31, 34, 36, 37, 39, 43, 45, 47, 49, 50, 54, 57, 61, 68, 69, 71, 74, 77, 81, 83, 86, 94, 107, 113, 116, 131, 136, 144, 149, 200, 216, 272, 296, 344, 376, 464, 544, 576, 800, 864, 1088, 1184, 1376, 1504, 1856, 2176, 2304, 3200, 3456, 4352, 4736, 5504, 6016, 7424
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OFFSET

1,1


COMMENTS

Conjecture: the even members of this sequence are all numbers of the form
k*4^m for k in [9,17,29], m>= 1, or k*4^m for k in [34, 50, 54, 74, 86, 94], m>=0.  Robert Israel, Nov 03 2017


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..77 (first 71 terms from Robert Price)
Eric Weisstein's World of Mathematics, Square Number
Index entries for sequences related to sums of squares


FORMULA

{n: A025428(n) = 2}.  R. J. Mathar, Jun 15 2018


MAPLE

N:= 10000: # to get all terms <= N
T:= Vector(N):
for a from 1 to floor(sqrt(N/4)) do
for b from a to floor(sqrt((Na^2)/3)) do
for c from b to floor(sqrt((Na^2b^2)/2)) do
for d from c to floor(sqrt(Na^2b^2c^2)) do
m:= a^2+b^2+c^2+d^2;
T[m]:= T[m]+1;
od od od od:
select(i > T[i] = 2, [$1..N]); # Robert Israel, Nov 03 2017


MATHEMATICA

M = 1000;
Clear[T]; T[_] = 0;
For[a = 1, a <= Floor[Sqrt[M/4]], a++,
For[b = a, b <= Floor[Sqrt[(M  a^2)/3]], b++,
For[c = b, c <= Floor[Sqrt[(M  a^2  b^2)/2]], c++,
For[d = c, d <= Floor[Sqrt[M  a^2  b^2  c^2]], d++,
m = a^2 + b^2 + c^2 + d^2;
T[m] = T[m] + 1;
]]]];
Select[Range[M], T[#] == 2&] (* JeanFrançois Alcover, Mar 22 2019, after Robert Israel *)


CROSSREFS

Cf. A025367 (at least 2 ways).
Sequence in context: A041479 A194380 A269267 * A095473 A095467 A095461
Adjacent sequences: A025355 A025356 A025357 * A025359 A025360 A025361


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



