OFFSET
0,5
COMMENTS
For a guide to related sequences, see A211795.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) + A212240(n) = n^4.
a(n) = Sum_{k=1..n-1} Sum_{i=1..n-1} d(k) * floor((n-k-1)/i), where d(k) is the number of divisors of k (A000005). - Wesley Ivan Hurt, Nov 16 2017
G.f.: (x/(1-x))*(Sum_{i>=1} x^i/(1-x^i))^2. - Robert Israel, Nov 16 2017
from Ridouane Oudra, Oct 10 2023: (Start)
a(n) = Sum_{i=1..n-1} Sum_{j=1..n-1} tau(i*j)*floor((n-1)/(i+j)) ;
a(n) = Sum_{i=1..n-1} Sum_{j=1..i-1} tau(j)*tau(i-j) ;
a(n+2) = Sum_{i=1..n} A055507(i). (End)
MAPLE
N:= 100: # to get a(0)..a(N)
g:= z*(1-z)^(-1)*add(z^i/(1-z^i), i=1..N-2)^2:
S:=series(g, z, N+1):
seq(coeff(S, z, n), n=0..N); # Robert Israel, Nov 16 2017
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w*x + y*z < n, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212151 *)
(* Peter J. C. Moses, Apr 13 2012 *)
PROG
(Python)
from sympy import divisor_count
def A212151(n): return sum((sum(divisor_count(i+1)*divisor_count(j-i) for i in range(j>>1))<<1)+(divisor_count(j+1>>1)**2 if j&1 else 0) for j in range(1, n-1)) # Chai Wah Wu, Jul 26 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 07 2012
STATUS
approved