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Number of even nontotients not exceeding 2^n.
2

%I #13 Jun 20 2024 02:38:44

%S 0,0,0,1,2,6,17,41,94,215,470,1004,2126,4449,9278,19177,39388,80698,

%T 164808,335809,683117,1387415,2813664,5700228,11536241,23324624,

%U 47122764,95134678,191937316,387024829,780018815,1571331010,3164113363

%N Number of even nontotients not exceeding 2^n.

%C Number of terms in A005277 <= 2^n.

%e For n = 6: a(6) = 6 because the even nontotients not exceeding 64 are {14,26,34,38,50,62}.

%t a = Table[0, {2^26}]; Do[ b = EulerPhi[n]; If[ EvenQ[b] && b < 2^27, a[[b/2]]++ ], {n, 3, 10^9}]; c = 0; k = 1; Do[ While[k <= 2^n, If[ a[[k]] == 0, c++ ]; k++ ]; Print[c], {n, 1, 17}]

%o (PARI) lista(kmax) = {my(c = 0, p = 2); forstep(k = 2, kmax, 2, if(!istotient(k), c++); if(k == p, print1(c, ", "); p *= 2));} \\ _Amiram Eldar_, Jun 20 2024

%Y Cf. A000079, A005277.

%K nonn,hard,more

%O 1,5

%A _Labos Elemer_, Jun 13 2002

%E Edited and extended by _Robert G. Wilson v_, Jul 15 2002

%E a(27)-a(32) from _Donovan Johnson_, Jun 03 2013

%E a(33) from _Amiram Eldar_, Jun 20 2024