A368674 Sum of the squarefree numbers less than n that do not divide n.

0, 0, 2, 3, 5, 5, 16, 21, 20, 16, 33, 33, 44, 48, 63, 84, 86, 92, 103, 105, 112, 130, 165, 177, 183, 173, 211, 191, 214, 202, 273, 302, 290, 318, 359, 395, 406, 422, 465, 503, 520, 508, 603, 611, 623, 621, 692, 728, 732, 722, 719, 749, 790, 832, 827, 875, 876, 924, 1013, 1001

Offset

1,3

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = Sum_{k=1..n} k * mu(k)^2 * (ceiling(n/k) - floor(n/k)).

Example

a(12) = 33. There are 4 squarefree numbers less than 12 that do not divide 12, namely: 5, 7, 10, and 11. Their sum is 5 + 7 + 10 + 11 = 33.

Mathematica

Table[Sum[k*MoebiusMu[k]^2 (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}]

Prog

(PARI) a(n) = sum(k=1, n-1, if ((n % k) && issquarefree(k), k)); \\ Michel Marcus, Jan 03 2024

Crossrefs

Cf. A008683 (mu), A368673.

Sequence in context: A342437 A079022 A368706 * A095296 A256301 A226609

Adjacent sequences: A368671 A368672 A368673 * A368675 A368676 A368677

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 02 2024

Status

approved