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A367326 a(n) = Sum_{(n - k)|n} k^2.

%I A367326 #35 Nov 14 2023 17:55:30
%S A367326 0,0,1,4,13,16,50,36,101,100,170,100,402,144,362,440,629,256,995,324,
%T A367326 1266,920,962,484,2578,976,1370,1576,2618,784,4180,900,3477,2408,2402,
%U A367326 2840,7023,1296,3026,3416,7810,1600,8548,1764,6786,7496,4490,2116,14546
%N A367326 a(n) = Sum_{(n - k)|n} k^2.
%F A367326 a(n) = n^2*A000005(n) - 2*n*A000203(n) + A001157(n) for n >= 1. - _Chai Wah Wu_, Nov 14 2023
%p A367326 divides := (k, n) -> k = n or (k > 0 and irem(n, k) = 0):
%p A367326 a := n -> local d; add(`if`(divides(n - d, n), d^2, 0), d = 0..n-1):
%p A367326 seq(a(n), n = 0..61);
%t A367326 a[0] = 0; a[n_] := DivisorSum[n, (n - #)^2 &]; Array[a, 50, 0]
%t A367326 (* _Amiram Eldar_, Nov 14 2023 *)
%t A367326 a[n_] := Sum[If[Divisible[n, n - k], k^2, 0], {k, 0, n - 1}]
%t A367326 Table[a[n], {n, 0, 48}]  (* _Peter Luschny_, Nov 14 2023 *)
%o A367326 (SageMath)
%o A367326 def A367326(n): return sum(k^2 for k in (0..n) if (n-k).divides(n))
%o A367326 print([A367326(n) for n in range(50)])
%o A367326 (Julia)
%o A367326 using AbstractAlgebra
%o A367326 function A367326(n)
%o A367326     sum(k^2 for k in 0:n if is_divisible_by(n, n - k))
%o A367326 end
%o A367326 [A367326(n) for n in 0:48] |> println
%o A367326 (PARI)
%o A367326 a(n) = if(n == 0, 0, sumdiv(n, d, (n-d)^2)); \\ _Michel Marcus_, Nov 14 2023
%o A367326 (Python)
%o A367326 from math import prod
%o A367326 from sympy import factorint
%o A367326 def A367326(n):
%o A367326     f = factorint(n).items()
%o A367326     return n*(n*prod(e+1 for p,e in f) - (prod((p**(e+1)-1)//(p-1) for p,e in f)<<1))+prod((p**(e+1<<1)-1)//(p**2-1) for p,e in f) if n else 0
%o A367326 # _Chai Wah Wu_, Nov 14 2023
%Y A367326 Cf. A094471, A001157, A007434.
%K A367326 nonn
%O A367326 0,4
%A A367326 _Peter Luschny_, Nov 14 2023