A069177 Maximal power of 2 that divides Phi(n), or the size of the Sylow 2-subgroup of the group of units mod n.

1, 1, 2, 2, 4, 2, 2, 4, 2, 4, 2, 4, 4, 2, 8, 8, 16, 2, 2, 8, 4, 2, 2, 8, 4, 4, 2, 4, 4, 8, 2, 16, 4, 16, 8, 4, 4, 2, 8, 16, 8, 4, 2, 4, 8, 2, 2, 16, 2, 4, 32, 8, 4, 2, 8, 8, 4, 4, 2, 16, 4, 2, 4, 32, 16, 4, 2, 32, 4, 8, 2, 8, 8, 4, 8, 4, 4, 8, 2, 32, 2, 8, 2, 8, 64, 2, 8, 8, 8, 8, 8, 4, 4, 2, 8, 32

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2^A053574(n). Multiplicative with a(2^e) = 2^(e-1) and a(p^e) = power of 2 in prime factorization of p - 1 for an odd prime p. - Vladeta Jovovic, Apr 10 2002

Mathematica

Table[2^IntegerExponent[EulerPhi@ n, 2], {n, 96}] (* Michael De Vlieger, Aug 23 2017 *)

Prog

(Scheme) (define (A069177 n) (cond ((= 1 n) n) ((zero? (modulo n 4)) (* 2 (A069177 (/ n 2)))) ((even? n) (A069177 (/ n 2))) (else (* (A006519 (+ -1 (A020639 n))) (A069177 (A028234 n)))))) ;; (After Jovovic's multiplicative formula) - Antti Karttunen, Aug 22 2017
(PARI) a(n) = 2^valuation(eulerphi(n), 2); \\ Amiram Eldar, Sep 05 2023

Crossrefs

Cf. A000010, A006519, A053574, A023506.

Sequence in context: A088200 A073103 A247257 * A077659 A367953 A212595

Adjacent sequences: A069174 A069175 A069176 * A069178 A069179 A069180

Keyword

nonn,easy,mult

Author

Sharon Sela (sharonsela(AT)hotmail.com), Apr 09 2002

Extensions

More terms from Vladeta Jovovic, Apr 10 2002

Status

approved