%I #7 Jan 24 2024 12:18:52

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

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

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

%N The number of unitary divisors of n that are squares of primes.

%C The number of exponents in the prime factorization of n that are equal to 2.

%H Amiram Eldar, <a href="/A369427/b369427.txt">Table of n, a(n) for n = 1..10000</a>

%F Additive with a(p^e) = 1 if e = 2, and 0 otherwise.

%F a(n) > 0 if and only if n is in A038109.

%F a(A061742(n)) = n, and a(k) < n for all k < A061742(n).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} (1/p^2 - 1/p^3) = A085548 - A085541 = 0.27748478074162196208... .

%t f[p_, e_] := If[e == 2, 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

%o (PARI) a(n) = vecsum(apply(x -> if(x == 2, 1, 0), factor(n)[, 2]));

%Y Cf. A001248, A038109, A056169, A056170, A061742, A085541, A085548.

%Y Similar sequences: A125070, A293439, A366074, A367512, A369426, A369428.

%K nonn,easy

%O 1,36

%A _Amiram Eldar_, Jan 23 2024