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

Author

Wesley Ivan Hurt, Jan 02 2024

Keywords

• nonn
• easy

Examples

			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.
		

Crossrefs

Cf. A008683 (mu), A368673.

Programs

Mathematica

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

PARI

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

Formula

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