cp's OEIS Frontend

A366146 The sum of divisors of the largest divisor of n that is a cubefull number (A036966).

%I A366146 #9 Oct 02 2023 01:44:26
%S A366146 1,1,1,1,1,1,1,15,1,1,1,1,1,1,1,31,1,1,1,1,1,1,1,15,1,1,40,1,1,1,1,63,
%T A366146 1,1,1,1,1,1,1,15,1,1,1,1,1,1,1,31,1,1,1,1,1,40,1,15,1,1,1,1,1,1,1,
%U A366146 127,1,1,1,1,1,1,1,15,1,1,1,1,1,1,1,31,121,1
%N A366146 The sum of divisors of the largest divisor of n that is a cubefull number (A036966).
%H A366146 Amiram Eldar, <a href="/A366146/b366146.txt">Table of n, a(n) for n = 1..10000</a>
%F A366146 a(n) = A000203(A360540(n)).
%F A366146 a(n) = A000203(n)/A366148(n).
%F A366146 a(n) >= 1, with equality if and only if n is cubefree (A004709).
%F A366146 a(n) <= A000203(n), with equality if and only if n is cubefull (A036966).
%F A366146 Multiplicative with a(p^e) = 1 if e <= 2 and (p^(e+1)-1)/(p-1) otherwise.
%F A366146 Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(3*s-3) + 1/p^(3*s-2) + 1/p^(3*s-1) - 1/p^(4*s-3) - 1/p^(4*s-2)).
%t A366146 f[p_, e_] := If[e < 3, 1, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A366146 (PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, if(e[i] < 3, 1, (p[i]^(e[i]+1)-1)/(p[i]-1)))};
%Y A366146 Cf. A000203, A036966, A295294, A360540, A366076, A366145, A366148.
%K A366146 nonn,easy,mult
%O A366146 1,8
%A A366146 _Amiram Eldar_, Oct 01 2023