A072077 Number of even nontotients not exceeding 2^n.

0, 0, 0, 1, 2, 6, 17, 41, 94, 215, 470, 1004, 2126, 4449, 9278, 19177, 39388, 80698, 164808, 335809, 683117, 1387415, 2813664, 5700228, 11536241, 23324624, 47122764, 95134678, 191937316, 387024829, 780018815, 1571331010, 3164113363

Offset: 1

Author

Labos Elemer, Jun 13 2002

Keywords

• nonn
• hard
• more

Comments

Number of terms in A005277 <= 2^n.

Examples

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

Crossrefs

Cf. A000079, A005277.

Programs

Mathematica

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}]

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

Extensions

Edited and extended by Robert G. Wilson v, Jul 15 2002

a(27)-a(32) from Donovan Johnson, Jun 03 2013

a(33) from Amiram Eldar, Jun 20 2024