A168649 a(n) = (1/n)*Sum_{d|n} moebius(d)*2^(n^2/d).

2, 6, 168, 16320, 6710880, 11453201760, 80421421917312, 2305843008676823040, 268650182136584246132736, 126765060022822827559679531520, 241677817415439249618874010960062464, 1858395433210885261794249658823668075069440

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..57

Formula

a(n) = (1/n)*Sum_{d|n} moebius(n/d)*(2^n)^d.

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] * 2^(n^2/#) &] / n; Array[a, 10] (* Amiram Eldar, Aug 18 2023 *)

Prog

(PARI) a(n)=(1/n)*sumdiv(n, d, moebius(d)*2^(n^2/d))
(Magma)
A168649:= func< n | (&+[MoebiusMu(Floor(n/d))*(2^n)^d: d in Divisors(n)])/n >;
[A168649(n): n in [1..40]]; // G. C. Greubel, Apr 08 2025
(SageMath)
def A168649(n): return sum( moebius(n//k)*(2^n)^k for k in (1..n) if (k).divides(n))//n
print([A168649(n) for n in range(1, 41)]) # G. C. Greubel, Apr 08 2025

Crossrefs

Cf. A001037, A008683.

Sequence in context: A329980 A199482 A382212 * A135937 A182523 A137532

Adjacent sequences: A168646 A168647 A168648 * A168650 A168651 A168652

Keyword

nonn

Author

Paul D. Hanna, Dec 01 2009

Extensions

a(12) from Amiram Eldar, Aug 18 2023

Status

approved