A368679 Sum of the squarefree values of (n-k) where the numbers k are the numbers less than n that do not divide n.

0, 0, 1, 1, 6, 3, 11, 11, 18, 19, 24, 18, 45, 38, 48, 58, 87, 72, 104, 79, 109, 112, 144, 123, 189, 176, 189, 154, 215, 200, 244, 244, 253, 288, 308, 275, 407, 388, 418, 379, 521, 426, 562, 507, 575, 624, 647, 605, 698, 740, 706, 675, 791, 740, 844, 802, 861, 870, 956

Offset

1,5

Links

Table of n, a(n) for n=1..59.

Formula

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

Example

a(12) = 18. The numbers k that are less than 12 and do not divide 12 are: {5,7,8,9,10,11}. The corresponding n-k values are: {7,5,4,3,2,1} (only 5 of which are squarefree). The sum of the squarefree values of n-k is then 7+5+3+2+1 = 18.

Mathematica

Table[Sum[(n - k) MoebiusMu[n - 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(n-k), n-k)); \\ Michel Marcus, Jan 03 2024

Crossrefs

Cf. A008683 (mu), A368677, A368680.

Sequence in context: A060534 A060445 A131894 * A335393 A040033 A165998

Adjacent sequences: A368676 A368677 A368678 * A368680 A368681 A368682

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 02 2024

Status

approved