|
%I #18 Sep 05 2021 07:39:05
%S 1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,2,2,1,3,1,2,2,2,
%T 1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,3,1,3,1,3,
%U 2,2,1,4,1,2,2,3,1,3,1,3,2,2,1,4,1,2,2,3,1,3,1,3,2,2,1,4,1,2,2,3,1,3,1,3,2
%N Number of divisors of n that are at most n^(1/3).
%H Seiichi Manyama, <a href="/A347516/b347516.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=1} x^(k^3)/(1 - x^k).
%t a[n_] := DivisorSum[n, 1 &, # <= n^(1/3) &]; Array[a, 100] (* _Amiram Eldar_, Sep 04 2021 *)
%o (PARI) a(n) = sumdiv(n, d, d^3<=n);
%o (PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/3), x^k^3/(1-x^k)))
%Y Cf. A000005, A010057, A038548, A347517.
%K nonn
%O 1,8
%A _Seiichi Manyama_, Sep 04 2021
|
