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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).

%I A362624 #37 Feb 16 2025 08:34:05
%S A362624 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 A362624 60,37,63,31,140,33,49,65,76,63,91,39,84,75,91,43,180,45,91,91,100,49,
%U A362624 125,57,124,95,105,55,148,91,117,105,124,61,245,63,132,117,97,105,260,69,133
%N A362624 a(n) = Sum_{d|n, gcd(d,n/d)=1} psi(d), where psi is the Dedekind psi function (A001615).
%H A362624 Amiram Eldar, <a href="/A362624/b362624.txt">Table of n, a(n) for n = 1..10000</a>
%H A362624 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>.
%H A362624 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dedekind_psi_function">Dedekind psi function</a>.
%F A362624 a(p) = p + 2, p prime.
%F A362624 From _Amiram Eldar_, May 03 2023: (Start)
%F A362624 Multiplicative with a(p^e) = 1 + (p+1)*p^(e-1).
%F A362624 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 A362624 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 A362624 Cf. A001615 (psi), A034444, A060648.
%K A362624 nonn,easy,mult
%O A362624 1,2
%A A362624 _Wesley Ivan Hurt_, Apr 28 2023