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A374457 The Dedekind psi function values of the exponentially odd numbers (A268335).

%I A374457 #7 Jul 10 2024 02:58:20
%S A374457 1,3,4,6,12,8,12,18,12,14,24,24,18,20,32,36,24,48,42,36,30,72,32,48,
%T A374457 48,54,48,38,60,56,72,42,96,44,72,48,72,54,108,72,96,80,90,60,62,96,
%U A374457 84,144,68,96,144,72,74,114,96,168,80,126,84,108,132,120,144,90
%N A374457 The Dedekind psi function values of the exponentially odd numbers (A268335).
%H A374457 Amiram Eldar, <a href="/A374457/b374457.txt">Table of n, a(n) for n = 1..10000</a>
%F A374457 a(n) = A001615(A268335(n)).
%F A374457 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 / A065463^2 = 2.01515877170903249510... .
%t A374457 f[p_, e_] := If[OddQ[e], (p+1) * p^(e-1), 0]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 100], # > 0 &]
%o A374457 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2] % 2, (f[i, 1]+1) * f[i, 1]^(f[i, 2] - 1), 0));}
%o A374457 lista(kmax) = {my(s1); for(k = 1, kmax, s1 = s(k); if(s1 > 0, print1(s1, ", ")));}
%Y A374457 Cf. A001615, A065463, A268335.
%Y A374457 Similar sequences related to psi: A000082, A033196, A323332, A371413, A371415.
%Y A374457 Similar sequences related to exponentially odd numbers: A366438, A366439, A366534, A366535, A367417, A368711, A374456.
%K A374457 nonn,easy
%O A374457 1,2
%A A374457 _Amiram Eldar_, Jul 09 2024