A345276 a(n) = Sum_{d|n} (n-d)^abs(mu(n/d)).

0, 1, 2, 3, 4, 12, 6, 6, 7, 22, 10, 26, 12, 32, 36, 11, 16, 38, 18, 46, 52, 52, 22, 52, 21, 62, 20, 66, 28, 168, 30, 20, 84, 82, 92, 77, 36, 92, 100, 92, 40, 240, 42, 106, 110, 112, 46, 102, 43, 112, 132, 126, 52, 112, 148, 132, 148, 142, 58, 340, 60, 152, 158, 37, 176, 384, 66

Offset

1,3

Comments

If p is prime, a(p) = Sum_{d|p} (p-d)^abs(mu(p/d)) = (p-1)^1 = p-1.

Links

Table of n, a(n) for n=1..67.

Example

a(12) = Sum_{d|12} (12-d)^abs(mu(12/d)) = 11^0 + 10^1 + 9^0 + 8^1 + 6^1 + 0^1 = 26.

Mathematica

Table[Sum[(n - k)^Abs[MoebiusMu[n/k]] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Cf. A008683 (mu).

Sequence in context: A370365 A099527 A354371 * A096864 A373576 A013620

Adjacent sequences: A345273 A345274 A345275 * A345277 A345278 A345279

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 12 2021

Status

approved