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%I #26 May 17 2023 11:13:25
%S 1,1,3,4,7,3,11,10,14,7,19,12,23,11,21,24,31,14,35,28,33,19,43,30,52,
%T 23,54,44,55,21,59,56,57,31,77,56,71,35,69,70,79,33,83,76,98,43,91,72,
%U 114,52,93,92,103,54,133,110,105,55,115,84,119,59,154,128,161,57,131
%N a(n) = Sum_{d|n} tau(d)*phi(d)*mu(n/d).
%C Möbius transform of tau(n)*phi(n) (A062355).
%H Amiram Eldar, <a href="/A359954/b359954.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Multiplicative with a(p) = 2*p - 3 and a(p^e) = (e*p + p - e)*(p - 1)*p^(e - 2) for e > 1. - _Amiram Eldar_, May 16 2023
%t f[p_, e_] := If[e == 1, 2*p - 3, (e*p + p - e)*(p - 1)*p^(e - 2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 16 2023 *)
%o (PARI) a(n) = sumdiv(n, d, numdiv(d)*eulerphi(d)*moebius(n/d)); \\ _Michel Marcus_, May 13 2023
%Y Cf. A000005 (tau), A000010 (phi), A008683 (mu), A062355, A363012.
%K nonn,easy,mult
%O 1,3
%A _Wesley Ivan Hurt_, May 12 2023