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A348061
a(n) = Sum_{k=1..n, gcd(n,k) = 1} n / gcd(n,k-1).
2
1, 1, 4, 3, 16, 4, 36, 11, 34, 16, 100, 12, 144, 36, 64, 43, 256, 34, 324, 48, 144, 100, 484, 44, 396, 144, 304, 108, 784, 64, 900, 171, 400, 256, 576, 102, 1296, 324, 576, 176, 1600, 144, 1764, 300, 544, 484, 2116, 172, 1758, 396, 1024, 432, 2704, 304, 1600, 396, 1296, 784, 3364, 192
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (p^(2*e+1) - (p + 1) * p^(2*e-1) + 1) / (p + 1).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} (1 - 1/p^2 - 1/(1 + p + p^2)) = 0.1381393084... . - Amiram Eldar, Nov 18 2022
MATHEMATICA
Table[Sum[If[GCD[n, k] == 1, n/GCD[n, k - 1], 0], {k, n}], {n, 60}]
f[p_, e_] := (p^(2 e + 1) - (p + 1) p^(2 e - 1) + 1)/(p + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60]
PROG
(PARI) a(n) = sum(k=1, n, if (gcd(n, k)==1, n/gcd(n, k-1))); \\ Michel Marcus, Sep 27 2021
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Ilya Gutkovskiy, Sep 26 2021
STATUS
approved