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
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[2^IntegerExponent[EulerPhi@ n, 2], {n, 96}] (* Michael De Vlieger, Aug 23 2017 *) -
PARI
a(n) = 2^valuation(eulerphi(n), 2); \\ Amiram Eldar, Sep 05 2023
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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
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
Extensions
More terms from Vladeta Jovovic, Apr 10 2002