A211508 Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2=n-x*y.

0, 0, 1, 2, 2, 4, 4, 6, 5, 6, 8, 8, 8, 12, 8, 10, 12, 12, 11, 16, 12, 16, 16, 12, 16, 20, 14, 16, 22, 20, 16, 24, 17, 22, 24, 16, 22, 30, 16, 24, 30, 26, 20, 28, 26, 28, 32, 18, 26, 38, 21, 30, 36, 28, 28, 34, 30, 36, 34, 26, 34, 46, 20, 28, 46, 36, 32, 40, 30, 42, 40

Offset

0,4

Comments

For a guide to related sequences, see A211422.

Links

David Radcliffe, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{k=1..floor(sqrt(n))} A000005(n-k^2). - David Radcliffe, Apr 24 2026

Mathematica

t[n_] := t[n] = Flatten[Table[w^2 + x*y - n, {w, 1, n}, {x, 1, n}, {y, 1, n}]]
c[n_] := Count[t[n], 0]
t = Table[c[n], {n, 0, 80}]  (* A211508 *)

Prog

(Python)
from sympy import divisor_count as d
from math import isqrt
def A211508(n): return sum(d(n - k*k) for k in range(1, isqrt(n)+1)) # David Radcliffe, Apr 24 2026

Crossrefs

Cf. A211422, A000005.

Sequence in context: A145392 A034974 A048275 * A109874 A069345 A341948

Adjacent sequences: A211505 A211506 A211507 * A211509 A211510 A211511

Keyword

nonn,look

Author

Clark Kimberling, Apr 14 2012

Status

approved