A066671 a(n) is the largest power of 2 that divides phi(A066669(n)).

2, 2, 2, 4, 2, 2, 4, 2, 2, 4, 4, 4, 4, 4, 8, 4, 8, 8, 4, 4, 8, 2, 2, 4, 8, 4, 8, 8, 4, 2, 16, 4, 4, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 4, 2, 32, 8, 16, 16, 4, 2, 8, 16, 16, 8, 8, 2, 32, 16, 16, 8, 8, 4, 16, 4, 16, 16, 4, 8, 32, 16, 8, 16, 16, 2, 2, 16, 4, 8, 16, 4, 8, 2, 16, 8, 32, 4, 64, 32, 32

Offset: 1

Author

Labos Elemer, Dec 18 2001

Keywords

• nonn

Examples

			The first, 4th and 15th terms in A066669 are 7, 13 and 35; phi(7) = 2*3, phi(13) = 4*3, phi(35) = 24 = 8*3; the largest powers of 2 are 2, 4 and 8; so a(1) = 2, a(4) = 4, a(15) = 8.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A065966, A066669, A066670, A066672, A066673, A069177.

Programs

Mathematica

Select[Array[{#1/#2, #2} & @@ {#, 2^IntegerExponent[#, 2]} &@ EulerPhi@ # &, 200], PrimeQ@ First@ # &][[All, -1]] (* Michael De Vlieger, Dec 08 2018 *)

PARI

lista(nn) = {for (n=1, nn, en=eulerphi(n); if (isprime(p=en>>valuation(en, 2)), print1(en/p, ", ")););} \\ Michel Marcus, Jan 03 2017

Formula

From Amiram Eldar, Jul 18 2024: (Start)

a(n) = A069177(A066669(n)).

a(n) = 2^A066672(n). (End)

Extensions

Name corrected by Amiram Eldar, Jul 18 2024