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A340141 Numerators of the sequence whose Dirichlet convolution with itself yields sequence A160595(x) = phi(x)/gcd(phi(x), x-1).

%I A340141 #10 Dec 29 2020 20:38:11
%S A340141 1,1,1,7,1,3,1,25,11,7,1,19,1,11,7,363,1,31,1,43,5,19,1,63,19,23,61,3,
%T A340141 1,15,1,1335,9,31,23,189,1,35,23,139,1,29,1,115,23,43,1,867,27,127,31,
%U A340141 11,1,163,39,279,17,55,1,73,1,59,123,9923,5,-15,1,187,21,-9,1,615,1,71,127,19,29,47,1,1875,1363,79,1,203,31
%N A340141 Numerators of the sequence whose Dirichlet convolution with itself yields sequence A160595(x) = phi(x)/gcd(phi(x), x-1).
%H A340141 Antti Karttunen, <a href="/A340141/b340141.txt">Table of n, a(n) for n = 1..8191</a>
%H A340141 Antti Karttunen, <a href="/A340141/a340141.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A340141 (PARI)
%o A340141 up_to = 65537;
%o A340141 A160595(n) = { my(x=eulerphi(n)); x/gcd(x,n-1); };
%o A340141 DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d<n, u[d]*u[n/d], 0)))/2); u};
%o A340141 v340141rat = DirSqrt(vector(up_to, n, A160595(n)));
%o A340141 A340141(n) = numerator(v340141rat[n]);
%Y A340141 Cf. A046644 (denominators).
%Y A340141 Cf. A160595.
%Y A340141 Cf. also A340142, A340143.
%K A340141 sign,frac
%O A340141 1,4
%A A340141 _Antti Karttunen_, Dec 29 2020