This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A365489 #10 Apr 20 2025 08:50:49
%S A365489 1,4,4,4,4,16,4,4,4,16,4,16,4,16,16,7,4,16,4,16,16,16,4,16,4,16,4,16,
%T A365489 4,64,4,7,16,16,16,16,4,16,16,16,4,64,4,16,16,16,4,28,4,16,16,16,4,16,
%U A365489 16,16,16,16,4,64,4,16,16,7,16,64,4,16,16,64,4,16,4
%N A365489 The number of divisors of the smallest cube divisible by n.
%C A365489 The number of divisors of the cube root of the smallest cube divisible by n, A019555(n), is A365488(n).
%H A365489 Amiram Eldar, <a href="/A365489/b365489.txt">Table of n, a(n) for n = 1..10000</a>
%F A365489 a(n) = A000005(A053149(n)).
%F A365489 Multiplicative with a(p^e) = 3*ceiling(e/3) + 1.
%F A365489 Dirichlet g.f.: zeta(s) * zeta(3*s) * Product_{p prime} (1 + 3/p^s - 1/p^(3*s)).
%t A365489 f[p_, e_] := 3*Ceiling[e/3] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365489 (PARI) a(n) = vecprod(apply(x -> 3*((x-1)\3) + 4, factor(n)[, 2]));
%Y A365489 Cf. A000005, A019555, A053149, A365345, A365488.
%K A365489 nonn,easy,mult
%O A365489 1,2
%A A365489 _Amiram Eldar_, Sep 05 2023