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%I #15 Mar 04 2023 15:21:10
%S 1,1,3,2,10,1,21,4,9,2,55,2,78,3,4,8,136,3,171,4,6,5,253,4,50,6,27,6,
%T 406,4,465,16,10,8,12,6,666,9,12,8,820,6,903,10,12,11,1081,8,147,10,
%U 16,12,1378,9,20,12,18,14,1711,8,1830,15,18,32,24,10,2211,16,22,12,2485,12
%N First derivative of cyclotomic(n,x) evaluated at x=1.
%H Indranil Ghosh, <a href="/A092502/b092502.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = (phi(n)/2)*Product_{d|n} d^moebius(n/d), n>1.
%F a(1) = 1; a(p^e) = p * phi(p^e) / 2 for prime p; otherwise, a(n) = phi(n) / 2. - _Álvar Ibeas_, Jan 15 2023
%t Table[If[n>1,(EulerPhi[n]/2) * Product[d^MoebiusMu[n/d], {d, Divisors[n]}], 1], {n , 1, 72}] (* _Indranil Ghosh_, Mar 16 2017 *)
%o (PARI) f(n) = {my(r = 1); fordiv(n, d, r*=d^moebius(n/d)); r};
%o a(n) = if (n==1, 1, f(n)*eulerphi(n)/2); \\ _Indranil Ghosh_, Mar 16 2017; edited by _Michel Marcus_, Jan 16 2023
%Y Cf. A020500.
%K nonn
%O 1,3
%A _Vladeta Jovovic_, Apr 05 2004
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