A334621 - OEIS

%I #8 Sep 11 2020 11:41:04

%S 0,0,0,0,0,1,0,0,0,1,0,0,0,1,1,0,0,0,0,1,1,1,0,1,0,1,0,1,0,0,0,0,2,1,

%T 1,0,0,1,1,1,0,2,0,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,0,2,0,1,0,0,0,1,0,1,

%U 2,1,0,0,0,1,0,1,2,1,0,0,0,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1

%N Number of unitary prime divisors, p, of n such that n-p is squarefree.

%F a(n) = Sum_{p|n, p prime, gcd(p,n/p) = 1} mu(n-p)^2, where mu is the Moebius function (A008683).

%e a(10) = 1; 5 is a unitary prime divisor of 10 since gcd(5,2) = 1, and 10 - 5 = 5 (squarefree).

%e a(33) = 2; 3 is a unitary prime divisor of 33 since gcd(3,11) = 1, and 33 - 3 = 30 (squarefree).

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

%Y Cf. A005117 (squarefree numbers), A008683 (Moebius), A056169 (number of unitary prime divisors of n).

%K nonn,easy

%O 1,33

%A _Wesley Ivan Hurt_, Sep 09 2020