A372962 a(n) = Sum_{1 <= x_1, x_2, x_3 <= n} ( n/gcd(x_1, x_2, x_3, n) )^2.
1, 29, 235, 925, 3101, 6815, 16759, 29597, 57097, 89929, 160931, 217375, 371125, 486011, 728735, 947101, 1419569, 1655813, 2475739, 2868425, 3938365, 4666999, 6435815, 6955295, 9690601, 10762625, 13874563, 15502075, 20510309, 21133315, 28628191, 30307229, 37818785
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
-
Mathematica
f[p_, e_] := (p^(5*e+5) - p^(5*e+2) + p^2 - 1)/(p^5-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 21 2024 *)
-
PARI
a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^2*sigma(d, 5));
Formula
a(n) = Sum_{d|n} mu(n/d) * (n/d)^2 * sigma_5(d).
From Amiram Eldar, May 21 2024: (Start)
Multiplicative with a(p^e) = (p^(5*e+5) - p^(5*e+2) + p^2 - 1)/(p^5-1).
Dirichlet g.f.: zeta(s)*zeta(s-5)/zeta(s-2).
Sum_{k=1..n} a(k) ~ c * n^6 / 6, where c = zeta(6)/zeta(4) = 2*Pi^2/21 = 0.939962323... (1/A088246). (End)
a(n) = Sum_{d|n} phi(n/d) * (n/d)^4 * sigma_4(d^2)/sigma_2(d^2). - Seiichi Manyama, May 24 2024
a(n) = Sum_{1 <= x_1, x_2, x_3 <= n} ( gcd(x_1, n)/gcd(x_1, x_2, x_3, n) )^3. - Seiichi Manyama, May 25 2024