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%I #36 May 03 2023 09:12:33
%S 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,
%T 60,37,63,31,140,33,49,65,76,63,91,39,84,75,91,43,180,45,91,91,100,49,
%U 125,57,124,95,105,55,148,91,117,105,124,61,245,63,132,117,97,105,260,69,133
%N a(n) = Sum_{d|n, gcd(d,n/d)=1} psi(d), where psi is the Dedekind psi function (A001615).
%H Amiram Eldar, <a href="/A362624/b362624.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_psi_function">Dedekind psi function</a>.
%F a(p) = p + 2, p prime.
%F From _Amiram Eldar_, May 03 2023: (Start)
%F Multiplicative with a(p^e) = 1 + (p+1)*p^(e-1).
%F 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)
%t 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 *)
%Y Cf. A001615 (psi), A034444, A060648.
%K nonn,easy,mult
%O 1,2
%A _Wesley Ivan Hurt_, Apr 28 2023
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