A342154 Number of partitions of n^5 into two positive squares.

0, 0, 1, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 3, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 0, 5, 3, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 3, 0, 0, 3, 3, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 3, 3, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0, 18, 0, 0, 3, 0, 0, 0, 1, 3, 3, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 18, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 3, 1, 0, 5, 3, 0, 0, 3, 0

Offset

0,6

Comments

a(n) > 0 if and only if n is in A000404. - Robert Israel, Mar 03 2021

Links

Robert Israel, Table of n, a(n) for n = 0..3050

Index entries for sequences related to sums of squares

Formula

a(n) = A025426(A000584(n)).

Example

2^5 = 32 = 4^2 + 4^2. So a(2) = 1.
5^5 = 3125 = 10^2 + 55^2 = 25^2 + 50^2 = 38^2 + 41^2. So a(5) = 3.

Maple

f:= proc(n) local x, y, S;
      S:= map(t -> subs(t, [x, y]), [isolve(x^2+y^2=n^5)]);
      nops(select(t -> t[1] >= t[2] and t[2] > 0, S))
end proc:
map(f, [$0..200]); # Robert Israel, Mar 03 2021

Prog

(PARI) a(n) = my(cnt=0, m=n^5); for(k=1, sqrt(m/2), l=m-k*k; if(l>0&&issquare(l), cnt++)); cnt;

Crossrefs

Cf. A000404, A000584, A025426, A046080, A084888.

Sequence in context: A324864 A331509 A171913 * A074936 A035655 A353323

Adjacent sequences: A342151 A342152 A342153 * A342155 A342156 A342157

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 02 2021

Status

approved