cp's OEIS Frontend

A365332 The sum of divisors of the largest square dividing n.

%I A365332 #8 Sep 02 2023 03:16:12
%S A365332 1,1,1,7,1,1,1,7,13,1,1,7,1,1,1,31,1,13,1,7,1,1,1,7,31,1,13,7,1,1,1,
%T A365332 31,1,1,1,91,1,1,1,7,1,1,1,7,13,1,1,31,57,31,1,7,1,13,1,7,1,1,1,7,1,1,
%U A365332 13,127,1,1,1,7,1,1,1,91,1,1,31,7,1,1,1,31,121
%N A365332 The sum of divisors of the largest square dividing n.
%C A365332 All the terms are odd.
%C A365332 The number of these divisors is A365331(n).
%C A365332 The sum of divisors of the square root of the largest square dividing n is A069290(n).
%H A365332 Amiram Eldar, <a href="/A365332/b365332.txt">Table of n, a(n) for n = 1..10000</a>
%F A365332 a(n) = A000203(A008833(n)).
%F A365332 a(n) = 1 if and only if n is squarefree (A005117).
%F A365332 Multiplicative with a(p^e) = (p^(e + 1 - (e mod 2)) - 1)/(p - 1).
%F A365332 Dirichlet g.f.: zeta(s) * zeta(2*s-1) * zeta(2*s-2) / zeta(4*s-2).
%F A365332 Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = 5*zeta(3/2)/Pi^2 = 1.323444812234... .
%t A365332 f[p_, e_] := (p^(e + 1 - Mod[e, 2]) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365332 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]^(f[i,2] + 1 - f[i,2]%2) - 1)/(f[i,1] - 1));}
%Y A365332 Cf. A000203, A005117, A008833, A069290, A078434, A365331.
%K A365332 nonn,easy,mult
%O A365332 1,4
%A A365332 _Amiram Eldar_, Sep 01 2023