A365346 The sum of divisors of the smallest square divisible by n.
1, 7, 13, 7, 31, 91, 57, 31, 13, 217, 133, 91, 183, 399, 403, 31, 307, 91, 381, 217, 741, 931, 553, 403, 31, 1281, 121, 399, 871, 2821, 993, 127, 1729, 2149, 1767, 91, 1407, 2667, 2379, 961, 1723, 5187, 1893, 931, 403, 3871, 2257, 403, 57, 217, 3991, 1281, 2863
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
f[p_, e_] := (p^(e + 1 + Mod[e, 2]) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
-
PARI
a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]^(f[i,2] + 1 + f[i,2]%2) - 1)/(f[i,1] - 1));} -
PARI
a(n) = sigma(n*core(n)); \\ Michel Marcus, Sep 02 2023
Formula
Multiplicative with a(p^e) = (p^(e + 1 + (e mod 2)) - 1)/(p - 1).
Dirichlet g.f.: zeta(s) * zeta(2*s-2) * Product_{p prime} (1 + 1/p^(s-2) + 1/p^(s-1) - 1/p^(2*s-2)).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (Pi^2/45) * zeta(3) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 0.344306233314... .
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