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A362624
a(n) = Sum_{d|n, gcd(d,n/d)=1} psi(d), where psi is the Dedekind psi function (A001615).
1
1, 4, 5, 7, 7, 20, 9, 13, 13, 28, 13, 35, 15, 36, 35, 25, 19, 52, 21, 49, 45, 52, 25, 65, 31, 60, 37, 63, 31, 140, 33, 49, 65, 76, 63, 91, 39, 84, 75, 91, 43, 180, 45, 91, 91, 100, 49, 125, 57, 124, 95, 105, 55, 148, 91, 117, 105, 124, 61, 245, 63, 132, 117, 97, 105, 260, 69, 133
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Dedekind Function.
FORMULA
a(p) = p + 2, p prime.
From Amiram Eldar, May 03 2023: (Start)
Multiplicative with a(p^e) = 1 + (p+1)*p^(e-1).
Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1/p^2 + 1/p + p/(1 + p)) = 1.00068765086778318519... . (End)
MATHEMATICA
f[p_, e_] := 1 + (p + 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 03 2023 *)
CROSSREFS
Cf. A001615 (psi), A034444, A060648.
Sequence in context: A087202 A270037 A319132 * A322757 A010666 A196001
KEYWORD
nonn,easy,mult
AUTHOR
Wesley Ivan Hurt, Apr 28 2023
STATUS
approved