A363735 a(n) = Sum_{k=0..n} n^notdivides(k, n), where notdivides(k, n) = 0 if k divides n, otherwise 1.

1, 2, 4, 8, 11, 22, 22, 44, 44, 66, 74, 112, 90, 158, 158, 184, 197, 274, 240, 344, 306, 382, 422, 508, 416, 578, 602, 652, 650, 814, 698, 932, 870, 994, 1058, 1124, 1017, 1334, 1334, 1408, 1328, 1642, 1478, 1808, 1722, 1806, 1982, 2164, 1882, 2306, 2256, 2452

Offset

0,2

Links

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

Formula

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

a(n) + A363734(n) = (n + 1)^2.

a(n) - A363734(n) = A363421(n).

Mathematica

A363735[n_]:=If[n==0, 1, n(n+1)+(1-n)DivisorSigma[0, n]]; Array[A363735, 100, 0] (* Paolo Xausa, Aug 06 2023 *)

Prog

(SageMath)
print([sum(n^(not k.divides(n)) for k in srange(n + 1)) for n in srange(52)])
(Python)
from sympy import divisor_count
def A363735(n): return n*(n+1)-(n-1)*divisor_count(n) if n else 1 # Chai Wah Wu, Jun 28 2023

Crossrefs

Cf. A113704, A000005, A363734, A363421.

Sequence in context: A320440 A288149 A159693 * A053437 A018277 A004654

Adjacent sequences: A363732 A363733 A363734 * A363736 A363737 A363738

Keyword

nonn

Author

Peter Luschny, Jun 27 2023

Status

approved