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Expansion of g.f. Product_{k>=1} (1 - x^k)^phi(k), where phi() is the Euler totient function (A000010).
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%I #19 Aug 03 2021 02:14:11

%S 1,-1,-1,-1,0,0,3,1,4,2,3,-5,1,-13,-5,-13,-6,-22,12,-12,35,17,59,11,

%T 101,-1,81,-35,45,-165,29,-311,-69,-383,-57,-501,181,-501,425,-191,

%U 990,-70,1844,64,2305,183,2625,-951,2897,-2701,1845,-4851,664,-8824,670,-12366,269,-14137,2884

%N Expansion of g.f. Product_{k>=1} (1 - x^k)^phi(k), where phi() is the Euler totient function (A000010).

%H Seiichi Manyama, <a href="/A346770/b346770.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: exp(-Sum_{k>=1} A057660(k) * x^k/k).

%F a(0) = 1, a(n) = -(1/n) * Sum_{k=1..n} A057660(k) * a(n-k) for n > 0.

%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-x^k)^eulerphi(k)))

%o (PARI) N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, sigma(k^2, 2)/sigma(k^2)*x^k/k)))

%Y Convolution inverse of A061255.

%Y Cf. A000010, A057660, A293116, A299069.

%K sign

%O 0,7

%A _Seiichi Manyama_, Aug 02 2021