A053574 Exponent of 2 in phi(n) where phi(n) = A000010(n).

0, 0, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 3, 3, 4, 1, 1, 3, 2, 1, 1, 3, 2, 2, 1, 2, 2, 3, 1, 4, 2, 4, 3, 2, 2, 1, 3, 4, 3, 2, 1, 2, 3, 1, 1, 4, 1, 2, 5, 3, 2, 1, 3, 3, 2, 2, 1, 4, 2, 1, 2, 5, 4, 2, 1, 5, 2, 3, 1, 3, 3, 2, 3, 2, 2, 3, 1, 5, 1, 3, 1, 3, 6, 1, 3, 3, 3, 3, 3, 2, 2, 1, 3, 5, 5, 1, 2, 3, 2, 5, 1, 4, 4, 2, 1, 2, 2, 3, 3, 4, 4, 2, 3, 3, 3, 1, 5, 5

Offset: 1

Author

Labos Elemer, Jan 18 2000

Keywords

• nonn
• easy

Examples

			For n = 513 = 27*19, phi(513) = 4*81 so exponent of 2 is 2, thus a(513) = 2.
		

Links

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

Crossrefs

Cf. A000010, A007814, A053575, A286572.

Programs

Mathematica

IntegerExponent[Array[EulerPhi, 120], 2] (* Michael De Vlieger, Aug 16 2017 *)

PARI

vector(66,n,valuation(eulerphi(n),2)) \\ Joerg Arndt, Apr 22 2011

Formula

a(n) = A007814(A000010(n)).

A000010(n) = A053575(n) * 2^a(n). - Antti Karttunen, May 26 2017

Additive with a(2^e) = e-1, and a(p^e) = A007814(p-1) for an odd prime p. - Amiram Eldar, Sep 05 2023

Extensions

Data section extended to 120 terms by Antti Karttunen, May 26 2017