A337328 - OEIS

%I #3 Aug 23 2020 20:10:40

%S 1,3,3,3,3,10,3,3,3,10,3,10,3,10,10,3,3,10,3,10,10,10,3,10,3,10,3,10,

%T 3,36,3,3,10,10,10,10,3,10,10,10,3,36,3,10,10,10,3,10,3,10,10,10,3,10,

%U 10,10,10,10,3,36,3,10,10,3,10,36,3,10,10,36,3,10,3,10,10,10,10,36

%N Number of pairs of squarefree divisors of n, (d1,d2), such that d1 <= d2.

%F a(n) = Sum_{d1|n, d2|n, d1 and d2 squarefree, d1 <= d2} 1.

%e a(28) = 10; The divisors of 28 are {1,2,4,7,14,28}. The pairs of squarefree divisors of 28, (d1,d2), such that d1 <= d2 are (1,1), (1,2), (1,7), (1,14), (2,2), (2,7), (2,14), (7,7), (7,14) and (14,14). So a(28) = 10.

%e a(29) = 3; The divisors of 29 are {1,29}. The pairs of squarefree divisors of 29, (d1,d2), such that d1 <= d2 are (1,1), (1,29) and (29,29). So a(29) = 3.

%e a(30) = 36; The divisors of 30 are {1,2,3,5,6,10,15,30}. The 36 pairs of squarefree divisors of 30, (d1,d2) such that d1 <= d2 are (1,1), (1,2), (1,3), (1,5), (1,6), (1,10), (1,15), (1,30), (2,2), (2,3), (2,5), (2,6), (2,10), (2,15), (2,30), (3,3), (3,5), (3,6), (3,10), (3,15), (3,30), (5,5), (5,6), (5,10), (5,15), (5,30), (6,6), (6,10), (6,15), (6,30), (10,10), (10,15), (10,30), (15,15), (15,30), (30,30). So a(30) = 36.

%e a(31) = 3; The divisors of 31 are {1,31}. The pairs of squarefree divisors of 31 are (1,1), (1,31) and (31,31). So a(31) = 3.

%t Table[Sum[Sum[MoebiusMu[i]^2 MoebiusMu[k]^2*(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 100}]

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Aug 23 2020