A344575 - OEIS

A344575

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

1, 3, 4, 7, 6, 12, 8, 14, 13, 18, 12, 26, 14, 24, 24, 27, 18, 38, 20, 38, 32, 36, 24, 52, 31, 42, 38, 50, 30, 72, 32, 52, 48, 54, 48, 77, 38, 60, 56, 76, 42, 96, 44, 74, 74, 72, 48, 102, 57, 92, 72, 86, 54, 112, 72, 100, 80, 90, 60, 148, 62, 96, 98, 101, 84, 144, 68, 110, 96

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..69.

FORMULA

a(8) = Sum_{d|8} d^abs(mu(8/d)) = 1^0 + 2^0 + 4^1 + 8^1 = 14.

MATHEMATICA

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

CROSSREFS