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
Examples
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.
Programs
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Mathematica
Table[Sum[(n - k) MoebiusMu[n - k]^2 (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}] -
PARI
a(n) = sum(k=1, n-1, if ((n % k) && issquarefree(n-k), n-k)); \\ Michel Marcus, Jan 03 2024
Formula
a(n) = Sum_{k=1..n} (n-k) * mu(n-k)^2 * (ceiling(n/k) - floor(n/k)).