A066671 Powers of 2 arising in A066669: a(n) is the largest even divisor of EulerPhi(A066669(n)), which by definition is a power of 2.

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

Example

First, 4th and 15th terms in A066669 are 7, 13, 35; phi(7) = 2*3, phi(13) = 4*3, phi(35) = 24 = 8*3; the largest even divisors (powers of 2) are 2, 4, 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.

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

Status

approved