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A350223
a(n) = Sum_{k=1..n} (-1)^(k+1) * floor((n/k)^k).
4
1, 1, 2, 1, 2, 1, 2, 0, 2, 2, 3, 0, 3, 2, 4, -1, 2, 1, 1, 0, 3, 2, 2, -2, 2, -1, 2, 2, 2, -1, 3, -1, 7, 2, 2, 0, 3, 2, 4, -2, 3, -1, 1, 1, 0, 3, 5, -1, 4, 1, 1, -2, 1, 1, 5, -2, 4, -1, 4, 0, 3, 1, 1, -1, 2, 1, 3, -1, 6, -1, 2, -5, 7, 0, 1, -1, 4, -2, 8, -5, 2, 4, 1, 3, 2, 4, 2, -3, 1, 0, 2, -1, 3, 4, 0, -6, 2, -1, 6, 3, 3, 1, 5, -6, 9
OFFSET
1,3
LINKS
EXAMPLE
a(3) = [3/1] - [(3/2)^2] + [(3/3)^3] = 3 - 2 + 1 = 2.
a(4) = [4/1] - [(4/2)^2] + [(4/3)^3] - [(4/4)^4] = 4 - 4 + 2 - 1 = 1.
MATHEMATICA
a[n_] := Sum[(-1)^(k + 1)*Floor[(n/k)^k], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, Dec 20 2021 *)
PROG
(PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n^k\k^k));
CROSSREFS
Sequence in context: A029445 A274920 A316828 * A274820 A230583 A197366
KEYWORD
sign
AUTHOR
Seiichi Manyama, Dec 20 2021
STATUS
approved