A347516 Number of divisors of n that are at most n^(1/3).
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, 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, 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
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := DivisorSum[n, 1 &, # <= n^(1/3) &]; Array[a, 100] (* Amiram Eldar, Sep 04 2021 *)
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PARI
a(n) = sumdiv(n, d, d^3<=n);
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PARI
N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/3), x^k^3/(1-x^k)))
Formula
G.f.: Sum_{k>=1} x^(k^3)/(1 - x^k).