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

0,2

Links

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

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).

Mathematica

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

Prog

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

Crossrefs

Cf. A113704, A000005, A363735, A363421.

Sequence in context: A075731 A009238 A009203 * A202273 A210702 A173177

Adjacent sequences: A363731 A363732 A363733 * A363735 A363736 A363737

Keyword

nonn

Author

Peter Luschny, Jun 27 2023

Status

approved