cp's OEIS Frontend

A380325 The sum of the square roots of the squares that divide the n-th exponentially odd number.

%I A380325 #8 Jan 22 2025 03:30:42
%S A380325 1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,3,1,4,1,1,1,7,1,1,1,1,1,1,3,1,1,1,
%T A380325 1,1,1,1,4,1,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,
%U A380325 7,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,3,1
%N A380325 The sum of the square roots of the squares that divide the n-th exponentially odd number.
%H A380325 Amiram Eldar, <a href="/A380325/b380325.txt">Table of n, a(n) for n = 1..10000</a>
%F A380325 a(n) = A069290(A268335(n)).
%F A380325 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(2) * A330596 / d = 1.74789521005721521109..., where d = A065463 is the asymptotic density of the exponentially odd numbers.
%t A380325 f[p_, e_] := If[OddQ[e], (p^((e+1)/2) - 1)/(p - 1), 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]
%o A380325 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] % 2, (f[i, 1]^((f[i, 2]+1)/2) - 1)/(f[i, 1] - 1), 0));}
%o A380325 list(lim) = select(x -> x > 0, vector(lim, i, s(i)));
%Y A380325 Cf. A013661, A065463, A069290, A268335, A330596, A380323, A380324.
%K A380325 nonn,easy
%O A380325 1,7
%A A380325 _Amiram Eldar_, Jan 20 2025