A363734 a(n) = Sum_{k=0..n} n^divides(k, n), where divides(k, n) = 1 if k divides n, otherwise 0.

0, 2, 5, 8, 14, 14, 27, 20, 37, 34, 47, 32, 79, 38, 67, 72, 92, 50, 121, 56, 135, 102, 107, 68, 209, 98, 127, 132, 191, 86, 263, 92, 219, 162, 167, 172, 352, 110, 187, 192, 353, 122, 371, 128, 303, 310, 227, 140, 519, 194, 345, 252, 359, 158, 479, 272, 497

Offset: 0

Author

Peter Luschny, Jun 27 2023

Keywords

• nonn

Links

• Peter Luschny, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A113704, A000005, A363735, A363421.

Programs

Mathematica

A363734[n_]:=If[n==0,0,n+1+(n-1)DivisorSigma[0,n]];Array[A363734,100,0] (* Paolo Xausa, Aug 06 2023 *)

Python

from sympy import divisor_count
def A363734(n): return (n-1)*divisor_count(n)+n+1 if n else 0 # Chai Wah Wu, Jun 28 2023

SageMath

print([sum(n^k.divides(n) for k in srange(n+1)) for n in srange(57)])

Formula

a(n) = (n - 1) * tau(n) + n + 1 for n >= 1, where tau = A000005.

a(n) + A363735(n) = (n + 1)^2.

A363735(n) - a(n) = A363421(n).