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A368706
Sum of the squarefree numbers that are less than n, not dividing n, and relatively prime to n.
1
0, 0, 2, 3, 5, 5, 16, 15, 14, 10, 33, 23, 44, 32, 47, 54, 86, 53, 103, 70, 77, 100, 165, 95, 158, 121, 169, 106, 214, 119, 273, 194, 196, 210, 269, 190, 406, 280, 334, 283, 520, 226, 603, 378, 407, 399, 692, 358, 620, 414, 499, 468, 790, 411, 682, 565, 601, 656, 1013
OFFSET
1,3
FORMULA
a(n) = Sum_{k=1..n} k * mu(k)^2 * floor(1/gcd(n,k)) * (ceiling(n/k) - floor(n/k)).
EXAMPLE
a(7) = 16. There are 4 squarefree numbers that are less than 7, do not divide 7, and relatively prime to 7: namely {2, 3, 5, 6}. Their sum is then 2 + 3 + 5 + 6 = 16.
MATHEMATICA
Table[Sum[k * MoebiusMu[k]^2 * Floor[1/GCD[n, k]] * (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 80}]
CROSSREFS
Cf. A008683 (mu), A368705.
Sequence in context: A146305 A342437 A079022 * A368674 A095296 A256301
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 03 2024
STATUS
approved