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%I #14 Sep 07 2017 02:46:23
%S 1,10,18,54,70,78,110,162,174,198,222,230,234,246,294,414,426,438,450,
%T 470,486,534,594,666,702,770,846,858,882,910,1070,1158,1218,1242,1314,
%U 1350,1458,1610,1722,1782,1794,1866,1914,1926,1938,1950,1998,2058,2106,2250,2442,2530,2538,2574,2590,2646,2886
%N Primitive elements of A290002.
%C Members k of A290002 such that k/2 is not in A290002.
%C Includes all members of A025192 except 2 and 6.
%H Robert Israel, <a href="/A291931/b291931.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 18 is in the sequence because psi(phi(18)) = phi(psi(18)) = 12 but psi(phi(9)) = 12 <> 4 = phi(psi(9)).
%p psi:= proc(n) n*mul((1+1/i[1]), i=ifactors(n)[2]) end:
%p A290002:= select(psi @ numtheory:-phi = numtheory:-phi @ psi, {$1..3000}):
%p sort(convert(A290002 minus map(`*`,A290002,2), list));
%t f[n_] := n Sum[MoebiusMu[d]^2/d, {d, Divisors@ n}]; With[{s = Select[Range[3000], f[EulerPhi@ #] == EulerPhi[f@ #] &]}, Select[s, FreeQ[s, #/2] &]] (* _Michael De Vlieger_, Sep 06 2017 *)
%Y Cf. A025192, A290002.
%K nonn
%O 1,2
%A _Robert Israel_, Sep 06 2017
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