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A372882
a(n) = Sum_{k=1..n} gcd(k^3,n).
2
1, 3, 5, 10, 9, 15, 13, 36, 33, 27, 21, 50, 25, 39, 45, 104, 33, 99, 37, 90, 65, 63, 45, 180, 145, 75, 261, 130, 57, 135, 61, 336, 105, 99, 117, 330, 73, 111, 125, 324, 81, 195, 85, 210, 297, 135, 93, 520, 385, 435, 165, 250, 105, 783, 189, 468, 185, 171, 117, 450
OFFSET
1,2
LINKS
László Tóth, Menon's identity and arithmetical sums representing functions of several variables, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 69, No. 1 (2011), pp. 97-110.
FORMULA
From Amiram Eldar, May 24 2024: (Start)
a(n) = n * Sum_{d|n} A000010(d)*A000189(d)/d (Tóth, 2011).
Multiplicative with a(p^e) = p^e * (1 + ((p-1)/p) * Sum_{i=1..e} p^(floor(2*i/3))). (End)
MATHEMATICA
a[n_] := Sum[GCD[k^3, n], {k, 1, n}]; Array[a, 100] (* Amiram Eldar, May 24 2024 *)
PROG
(PARI) a(n) = sum(k=1, n, gcd(k^3, n));
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 15 2024
STATUS
approved