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Numbers k such that 4 divides phi(k) (i.e., A000010(k)).
5

%I #18 Feb 12 2021 04:04:34

%S 5,8,10,12,13,15,16,17,20,21,24,25,26,28,29,30,32,33,34,35,36,37,39,

%T 40,41,42,44,45,48,50,51,52,53,55,56,57,58,60,61,63,64,65,66,68,69,70,

%U 72,73,74,75,76,77,78,80,82,84,85,87,88,89,90,91,92,93,95,96,97,99,100,101

%N Numbers k such that 4 divides phi(k) (i.e., A000010(k)).

%C Complement of A097987.

%C The asymptotic density of this sequence is 1 (Dressler, 1975). - _Amiram Eldar_, Feb 12 2021

%H Rémy Sigrist, <a href="/A172019/b172019.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert E. Dressler, <a href="http://www.numdam.org/item/?id=CM_1975__31_2_115_0">A property of the phi and sigma_j functions</a>, Compositio Mathematica, Vol. 31, No. 2 (1975), pp. 115-118.

%t Select[Range[200], Mod[EulerPhi[#], 4] == 0 &] (* _Geoffrey Critzer_, Nov 30 2014 *)

%o (PARI) is(n)=my(o=valuation(n, 2), p); (o>1 || !isprimepower(n>>o, &p) || p%4<2) && n>4 \\ _Charles R Greathouse IV_, Mar 05 2013

%Y Cf. A000010, A097987, A066499, A066498, A066500, A066502.

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Jan 22 2010