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The Euler phi function values of the powerful numbers, A000010(A001694(n)).
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%I #16 Sep 30 2019 07:17:11

%S 1,2,4,6,8,20,18,16,12,42,32,24,54,40,36,110,100,64,48,156,84,80,72,

%T 120,162,128,96,272,108,294,342,168,160,144,252,220,200,256,506,192,

%U 500,216,360,312,486,336,320,812,288,240,930,440,324,400,512,660,600

%N The Euler phi function values of the powerful numbers, A000010(A001694(n)).

%C The sum of the reciprocals of all the terms of this sequence is Murata's constant Product_{p prime}(1 + 1/(p-1)^2) (A065485).

%C Sequence is injective: no value occurs more than once. - _Amiram Eldar_ and _Antti Karttunen_, Sep 30 2019

%H Amiram Eldar, <a href="/A323333/b323333.txt">Table of n, a(n) for n = 1..10000</a>

%H Eckford Cohen, <a href="https://doi.org/10.1090/S0002-9939-1961-0132717-6">A property of Dedekind's psi-function</a>, Proceedings of the American Mathematical Society, Vol. 12, No. 6 (1961), p. 996.

%t EulerPhi /@ Join[{1}, Select[Range@ 1200, Min@ FactorInteger[#][[All, 2]] > 1 &]] (* after _Harvey P. Dale_ at A001694 *)

%o (PARI) lista(nn) = apply(x->eulerphi(x), select(x->ispowerful(x), vector(nn, k, k))); \\ _Michel Marcus_, Jan 11 2019

%Y Cf. A000010, A001694, A002618 (a subsequence), A065485, A082695, A112526, A323332.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jan 11 2019