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%I #18 Feb 24 2022 08:46:25
%S 1,3,10,11,109,12,1189,119,1297,131,141481,118,1543321,1429,15445,
%T 14159,183642229,1299,2003229469,14041,1837837,170039,238367471761,
%U 14158,23854956949,1854841,2186871697,1670761,309400794703549
%N Primitive part of A006190(n), n >= 1.
%C A006190(n) = Product_{k divides n} a(k), n >= 1.
%F a(n) = ((3-sqrt(13))/2)^phi(n)*cyclotomic(n, -(11 - 3*sqrt13)/2) for n >= 1 and a(1) = 1, where phi is Euler's totient A000010 and the coefficient table for the cyclotomic polynomials is given in A013595.
%F a(n) = Product_{d|n} A006190(d)^mu(n/d), where mu = A008683, n >= 1.
%t (* b = A006190 *) b[0] = 0; b[1] = 1; b[n_] := b[n] = 3*b[n-1] + b[n-2]; a[n_] := Product[b[d]^MoebiusMu[n/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Jan 20 2015 *)
%Y Cf. A000010, A006190, A008683, A013595.
%Y Cf. A061446, A008555, A105603.
%K nonn,easy
%O 1,2
%A _Wolfdieter Lang_, Jan 19 2015