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Expansion of Product_{k>=1} (1 - x^phi(k)), where phi is Euler's totient function.
1

%I #14 May 12 2022 13:10:15

%S 1,-2,-2,6,-4,2,6,-14,8,-2,4,-6,-16,38,-22,6,2,-10,2,6,60,-126,28,70,

%T -38,6,-38,70,-54,38,18,-74,-70,214,106,-426,186,54,-26,-2,-92,186,

%U -218,250,-66,-118,-104,326,466,-1258,500,258,-254,250,-368,486,-342,198

%N Expansion of Product_{k>=1} (1 - x^phi(k)), where phi is Euler's totient function.

%F Product_{k>=1} (1 - x^k)^A014197(k).

%t terms = 58;

%t S[m_] := S[m] = CoefficientList[Product[1 - x^EulerPhi[k],

%t {k, 1, m*terms}] + O[x]^terms, x];

%t S[m = 1];

%t S[m++];

%t While[S[m] != S[m - 1], m++];

%t S[m] (* _Jean-François Alcover_, May 12 2022 *)

%Y Cf. A000010 (phi), A014197, A120963, A280611.

%K sign

%O 0,2

%A _Seiichi Manyama_, May 31 2018