A342693 a(n) = Sum_{d|n} mu(d) * floor(n/d^2).

1, 2, 3, 3, 5, 5, 7, 6, 8, 8, 11, 8, 13, 11, 14, 12, 17, 12, 19, 15, 19, 17, 23, 16, 24, 20, 24, 21, 29, 19, 31, 24, 30, 26, 34, 24, 37, 29, 35, 29, 41, 29, 43, 33, 39, 35, 47, 32, 48, 36, 46, 39, 53, 36, 53, 41, 51, 44, 59, 38, 61, 47, 55, 48, 63, 44, 67, 51, 62, 50, 71, 48

Offset

1,2

Comments

For primes p, a(p) = Sum_{d|p} mu(d) * floor(p/d^2) = mu(1)*p + mu(p)*0 = p.

Links

Table of n, a(n) for n=1..72.

Example

a(12) = Sum_{d|12} mu(d) * floor(12/d^2) = mu(1)*12 + mu(2)*3 + mu(3)*1 + mu(4)*0 + mu(6)*0 + mu(12)*0 = 12 - 3 - 1 + 0 + 0 + 0 = 8.

Mathematica

Table[Sum[MoebiusMu[k] Floor[n/k^2] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]

Crossrefs

Cf. A008683 (mu).

Sequence in context: A325163 A348538 A185075 * A349338 A074399 A090302

Adjacent sequences: A342690 A342691 A342692 * A342694 A342695 A342696

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2021

Status

approved