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%I #18 Oct 16 2022 08:00:32
%S 1,3,8,6,24,24,48,12,24,72,120,48,168,144,192,24,288,72,360,144,384,
%T 360,528,96,120,504,72,288,840,576,960,48,960,864,1152,144,1368,1080,
%U 1344,288,1680,1152,1848,720,576,1584,2208,192,336,360,2304,1008,2808,216,2880,576,2880,2520,3480,1152,3720,2880,1152,96
%N a(n) = A003557(n) * A048250(n) * A173557(n).
%H Amiram Eldar, <a href="/A345052/b345052.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (p^2 - 1) * p^(e-1).
%F a(n) = A007434(n) / A003557(n) = A003557(n) * A048250(n) * A173557(n).
%F From _Amiram Eldar_, Oct 16 2022: (Start)
%F Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/Pi^2 = 0.202642... (A185197).
%F Sum_{n>=1} 1/a(n) = A065484.
%F a(n) = A000010(n) * A048250(n). (End)
%t f[p_, e_] := (p^2 - 1)*p^(e - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 16 2022 *)
%o (PARI) A345052(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i,1]^2)-1)*(f[i,1]^(f[i, 2]-1))); };
%Y Cf. A000010, A003557, A007434, A048250, A065484, A173557, A185197.
%K nonn,mult,easy
%O 1,2
%A _Antti Karttunen_, Jun 08 2021
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