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(PARI) a(n) = sum(k=1, n-1, (n % k) && issquarefree(n-k)); \\ Michel Marcus, Jan 03 2024
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a(12) = 5. The numbers less than 12 that do not divide 12 are: {5,7,8,9,10,11} with additive complements values of n-k: {7,5,4,3,2,1} (exactly 5 of which are squarefree).
Number of numbers k less than n and not dividing n such that n-k is squarefree.
0, 0, 1, 1, 3, 2, 4, 4, 5, 5, 6, 5, 8, 7, 8, 9, 11, 10, 12, 10, 12, 12, 14, 13, 16, 15, 16, 14, 17, 16, 18, 18, 18, 19, 20, 19, 23, 22, 23, 22, 26, 23, 27, 25, 27, 28, 29, 28, 30, 31, 30, 29, 32, 31, 33, 32, 33, 33, 35, 32, 37, 36, 37, 38, 39, 37, 40, 38, 40, 40, 43, 41, 45, 44, 45, 44
allocated for Wesley Ivan HurtNumber of numbers k less than n not dividing n such that n-k is squarefree.
0, 0, 1, 1, 3, 2, 4, 4, 5, 5, 6, 5, 8, 7, 8, 9, 11, 10, 12, 10, 12, 12, 14, 13, 16, 15, 16, 14, 17, 16, 18, 18, 18, 19, 20, 19, 23, 22, 23, 22, 26, 23, 27, 25, 27, 28, 29, 28, 30, 31, 30, 29, 32, 31, 33, 32, 33, 33, 35, 32, 37, 36, 37, 38, 39, 37, 40, 38, 40, 40, 43, 41, 45, 44, 45, 44
1,5
a(n) = Sum_{k=1..n} mu(n-k)^2 * (ceiling(n/k) - floor(n/k)).
a(12) = 5. The numbers less than 12 that do not divide 12 are: {5,7,8,9,10,11} with additive complements {7,5,4,3,2,1} (exactly 5 of which are squarefree).
Table[Sum[MoebiusMu[n - k]^2 (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}]
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nonn,easy
Wesley Ivan Hurt, Jan 02 2024
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