A367327 a(n) = Sum_{(n - k) does not divide n, 0 <= k < n} k^2.

0, 0, 0, 1, 1, 14, 5, 55, 39, 104, 115, 285, 104, 506, 457, 575, 611, 1240, 790, 1785, 1204, 1950, 2349, 3311, 1746, 3924, 4155, 4625, 4312, 6930, 4375, 8555, 6939, 9032, 10127, 10845, 7887, 14910, 14549, 15603, 12730, 20540, 15273, 23821, 20648, 21874, 26905

Offset: 0

Author

Peter Luschny, Nov 14 2023

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A367327, A000330, A024816.

Programs

Maple

divides := (k, n) -> k = n or (k > 0 and irem(n, k) = 0):
A367327 := n -> local k; add(`if`(divides(n - k, n), 0, k^2), k = 0..n - 1):
seq(A367327(n), n = 0..61);

Mathematica

a[n_] := Sum[If[Divisible[n, n - k], 0, k^2], {k, 0, n - 1}]
Table[a[n], {n, 0, 46}]

PARI

a(n) = sum(k=0, n-1, if (n % (n-k), k^2)); \\ Michel Marcus, Nov 15 2023

Python

from math import prod
from sympy import factorint
def A367327(n):
    f = factorint(n).items()
    return n*(n-1)*((n<<1)-1)//6-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 # Chai Wah Wu, Nov 14 2023

SageMath

def A367327(n): return sum(k^2 for k in (0..n-1) if not (n-k).divides(n))
print([A367327(n) for n in range(47)])

Formula

A367326(n+1) + a(n+1) = A000330(n).