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A345276 a(n) = Sum_{d|n} (n-d)^abs(mu(n/d)). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A339782 A176621 A099527 * A096864 A013620 A317498

Adjacent sequences:  A345273 A345274 A345275 * A345277 A345278 A345279

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 12 2021

STATUS

approved

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Last modified January 29 02:59 EST 2022. Contains 350672 sequences. (Running on oeis4.)