A342694 a(n) = Sum_{d|n} d * mu(d) * floor(n/d^2).

1, 2, 3, 2, 5, 4, 7, 4, 6, 6, 11, 3, 13, 8, 12, 8, 17, 4, 19, 10, 15, 12, 23, 6, 20, 14, 18, 14, 29, 2, 31, 16, 24, 18, 30, 12, 37, 20, 27, 15, 41, 16, 43, 22, 25, 24, 47, 15, 42, 16, 36, 26, 53, 16, 45, 21, 39, 30, 59, 8, 61, 32, 35, 32, 55, 19, 67, 34, 48, 19, 71, 24, 73, 38

Offset

1,2

Comments

If p is prime, a(p) = Sum_{d|p} d * mu(d) * floor(p/d^2) = 1*1*p + p*(-1)*0 = p.

Links

Table of n, a(n) for n=1..74.

Example

a(10) = Sum_{d|10} d * mu(d) * floor(10/d^2) = 1*1*10 + 2*(-1)*2 + 5*(-1)*0 + 10*1*0 = 6.

Mathematica

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

Crossrefs

Cf. A008683 (mu).

Sequence in context: A195637 A181861 A365099 * A212831 A072969 A139712

Adjacent sequences: A342691 A342692 A342693 * A342695 A342696 A342697

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2021

Status

approved