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A358345 a(n) is the number of even square divisors of n.

%I A358345 #13 Nov 12 2022 06:35:33
%S A358345 0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,2,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,2,0,0,
%T A358345 0,2,0,0,0,1,0,0,0,1,0,0,0,2,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,3,0,0,0,1,
%U A358345 0,0,0,2,0,0,0,1,0,0,0,2,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,2,0,0,0,2
%N A358345 a(n) is the number of even square divisors of n.
%C A358345 First differs from A235127 at n = 36.
%C A358345 The first position of k >= 0 in this sequence is A187941(k)^2.
%H A358345 Amiram Eldar, <a href="/A358345/b358345.txt">Table of n, a(n) for n = 1..10000</a>
%F A358345 a(n) = A046951(n) - A298735(n).
%F A358345 a(n) = 2 * A046951(n) - A046951(4*n).
%F A358345 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/24 (A222171).
%t A358345 f1[p_, e_] := Floor[e/2] + 1; f2[p_, e_] := If[p == 2, 1, Floor[e/2] + 1]; a[1] = 0; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) - Times @@ f2 @@@ fct; Array[a, 100]
%o A358345 (PARI) a(n) = {my(f = factor(n)); prod(i=1, #f~, 1+f[i,2]\2) - prod(i=1, #f~, if(f[i,1] == 2, 1, 1+f[i,2]\2))};
%o A358345 (PARI) a(n) = sumdiv(n, d, if (issquare(d) && !(d%2), 1)); \\ _Michel Marcus_, Nov 11 2022
%Y A358345 Cf. A016742, A046951, A187941, A222171, A235127, A298735.
%K A358345 nonn
%O A358345 1,16
%A A358345 _Amiram Eldar_, Nov 11 2022