A368679 - OEIS

%I #12 Jan 03 2024 05:29:38

%S 0,0,1,1,6,3,11,11,18,19,24,18,45,38,48,58,87,72,104,79,109,112,144,

%T 123,189,176,189,154,215,200,244,244,253,288,308,275,407,388,418,379,

%U 521,426,562,507,575,624,647,605,698,740,706,675,791,740,844,802,861,870,956

%N Sum of the squarefree values of (n-k) where the numbers k are the numbers less than n that do not divide n.

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

%e 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.

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

%o (PARI) a(n) = sum(k=1, n-1, if ((n % k) && issquarefree(n-k), n-k)); \\ _Michel Marcus_, Jan 03 2024

%Y Cf. A008683 (mu), A368677, A368680.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Jan 02 2024