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A069177 Maximal power of 2 that divides Phi(n), or the size of the Sylow 2-subgroup of the group of units mod n. 3

%I

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A069177/b069177.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%t Table[2^IntegerExponent[EulerPhi@ n, 2], {n, 96}] (* _Michael De Vlieger_, Aug 23 2017 *)

%o (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

%Y Cf. A000010, A006519, A053574, A023506.

%K nonn,mult

%O 1,3

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

%E More terms from _Vladeta Jovovic_, Apr 10 2002

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Last modified September 25 19:42 EDT 2020. Contains 337344 sequences. (Running on oeis4.)