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

1,1

Links

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

Formula

From Amiram Eldar, Jul 18 2024:

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A361289 A188903 A366534 * A159802 A329586 A255336

Adjacent sequences: A066668 A066669 A066670 * A066672 A066673 A066674

Keyword

nonn

Author

Labos Elemer, Dec 18 2001

Extensions

Name corrected by Amiram Eldar, Jul 18 2024

Status

approved