A343876 - OEIS

A343876

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

1, 3, 4, 10, 6, 47, 8, 28, 21, 117, 12, 118, 14, 219, 248, 72, 18, 177, 20, 274, 472, 519, 24, 284, 55, 717, 90, 494, 30, 992, 32, 176, 1136, 1209, 1272, 462, 38, 1503, 1576, 628, 42, 1806, 44, 1126, 834, 2187, 48, 664, 105, 685, 2672, 1538, 54, 639, 3096, 1100, 3328, 3453

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

a(6) = 6 * Sum_{d|6} d^mu(d) = 6 * (1^1 + 2^(-1) + 3^(-1) + 6^1) = 47.

MATHEMATICA

Table[n*Sum[i^MoebiusMu[i] (1 - Ceiling[n/i] + Floor[n/i]), {i, n}], {n, 80}]

PROG