A371084 - OEIS

%I #9 Mar 12 2024 20:13:22

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

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

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

%N a(n) = 1 if n is a nonsquarefree number not divisible by p^p for any prime p, otherwise 0.

%H Antti Karttunen, <a href="/A371084/b371084.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = (1-A008966(n)) * A359550(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (1 - 1/p^p) - 6/Pi^2 = 0.1140631325... . - _Amiram Eldar_, Mar 12 2024

%o (PARI)

%o A359550(n) = { my(f = factor(n)); prod(k=1, #f~, (f[k, 2]<f[k, 1])); };

%o A371084(n) = (!issquarefree(n) && A359550(n));

%Y Characteristic function of A371083.

%Y Cf. A008966, A059956, A359550.

%K nonn

%O 1

%A _Antti Karttunen_, Mar 12 2024