login
Number of divisors of n that are at most n^(1/4).
2

%I #15 Sep 06 2021 03:03:23

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,

%T 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,

%U 1,2,1,2,1,2,1,2,1,2,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3,1,2,2,2,1,3

%N Number of divisors of n that are at most n^(1/4).

%H Seiichi Manyama, <a href="/A347526/b347526.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=1} x^(k^4)/(1 - x^k).

%t a[n_] := DivisorSum[n, 1 &, # <= n^(1/4) &]; Array[a, 100] (* _Amiram Eldar_, Sep 05 2021 *)

%o (PARI) a(n) = sumdiv(n, d, d^4<=n);

%o (PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/4), x^k^4/(1-x^k)))

%Y Cf. A000005, A038548, A063775, A347516, A347527.

%K nonn

%O 1,16

%A _Seiichi Manyama_, Sep 05 2021