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A371492 a(n) = Sum_{1 <= x_1, x_2, x_3 <= n} ( gcd(x_1, n)/gcd(x_1, x_2, x_3, n) )^2. 4
1, 17, 91, 289, 701, 1547, 2647, 4769, 7705, 11917, 15731, 26299, 30421, 44999, 63791, 77473, 87857, 130985, 136459, 202589, 240877, 267427, 290951, 433979, 448201, 517157, 633187, 764983, 729989, 1084447, 951391, 1248929, 1431521, 1493569, 1855547, 2226745 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} phi(n/d) * (n/d)^2 * sigma_4(d^2)/sigma_2(d^2).
From Amiram Eldar, May 24 2024: (Start)
Multiplicative with a(p^e) = (p^(4*e+1)*(p+1)*(p^2+p+1) - p^(3*e+1)*(p^2+1) + p + 1)/((p^2+1)*(p^2+p+1)).
Dirichlet g.f.: zeta(s)*zeta(s-3)*zeta(s-4)/zeta(s-2)^2.
Sum_{k=1..n} a(k) ~ c * n^5 / 5, where c = zeta(2)*zeta(5)/zeta(3)^2 = 1.180448217... . (End)
MATHEMATICA
f[p_, e_] := (p^(4*e+1)*(p+1)*(p^2+p+1) - p^(3*e+1)*(p^2+1) + p + 1)/((p^2+1)*(p^2+p+1)); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 36] (* Amiram Eldar, May 24 2024 *)
PROG
(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*(n/d)^2*sigma(d^2, 4)/sigma(d^2, 2));
CROSSREFS
Sequence in context: A159676 A061971 A061222 * A228462 A217641 A213574
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 24 2024
STATUS
approved

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Last modified July 20 06:48 EDT 2024. Contains 374441 sequences. (Running on oeis4.)