A370239 The sum of divisors of n that are squares of squarefree numbers.
1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 5, 1, 1, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 26, 1, 10, 5, 1, 1, 1, 5, 1, 1, 1, 50, 1, 1, 1, 5, 1, 1, 1, 5, 10, 1, 1, 5, 50, 26, 1, 5, 1, 10, 1, 5, 1, 1, 1, 5, 1, 1, 10, 5, 1, 1, 1, 5, 1, 1, 1, 50, 1, 1, 26, 5, 1, 1, 1, 5, 10, 1, 1
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
f[p_, e_] := If[e == 1, 1, 1 + p^2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
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PARI
a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] == 1, 1, 1 + f[i,1]^2));}
Formula
Multiplicative with a(p) = 1 and a(p^e) = 1 + p^2 for e >= 2.
a(n) >= 1, with equality if and only if n is squarefree (A005117).
Dirichlet g.f.: zeta(s)*zeta(2*s-2)/zeta(4*s-4).
Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = 2*zeta(3/2)/Pi^2 = 0.5293779248... .
Comments