cp's OEIS Frontend

A380324 The sum of the squares dividing the n-th exponentially odd number.

%I A380324 #7 Jan 21 2025 18:19:53
%S A380324 1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,5,1,10,1,1,1,21,1,1,1,1,1,1,5,1,1,
%T A380324 1,1,1,1,1,10,1,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,
%U A380324 1,21,1,1,1,1,5,1,1,1,1,1,1,1,1,1,1,1,5
%N A380324 The sum of the squares dividing the n-th exponentially odd number.
%H A380324 Amiram Eldar, <a href="/A380324/b380324.txt">Table of n, a(n) for n = 1..10000</a>
%F A380324 a(n) = A035316(A268335(n)).
%t A380324 f[p_, e_] := If[OddQ[e], (p^(e+1) - 1)/(p^2 - 1), 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &]
%o A380324 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] % 2, (f[i, 1]^(f[i, 2]+1) - 1)/(f[i, 1]^2 - 1), 0));}
%o A380324 list(lim) = select(x -> x > 0, vector(lim, i, s(i)));
%Y A380324 Cf. A035316, A268335, A380323, A380325.
%K A380324 nonn,easy
%O A380324 1,7
%A A380324 _Amiram Eldar_, Jan 20 2025