A055736 Difference between number of prime factors of n and of phi(n).

0, 1, 0, 0, 0, 1, -1, 0, -1, 1, -1, 1, -1, 0, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, -1, 0, -1, 0, -1, 2, -2, 0, 0, 1, 0, 0, -1, 0, 0, 1, -1, 1, -2, 0, 0, 0, -1, 1, -2, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 2, -2, -1, 0, 0, 0, 1, -2, 1, 0, 1, -2, 0, -1, 0, 0, 0, -1, 1, -2, 1, -1, 0, -1, 1, 1, -1, 0, 0, -1

Offset

1,30

Comments

Prime factors counted without multiplicity. - Harvey P. Dale, Mar 03 2016

The first term with an absolute value greater than 2 is a(211); the first term with an absolute value greater than 3 is a(2311); the first term with an absolute value greater than 4 is a(43891). - Harvey P. Dale, Mar 03 2016

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = A001221(n) - A001221(A000010(n)).

Example

For n=105, phi(n)=48, with 3 or 2 prime factors respectively, so a(105) = 3 - 2 = 1.

Mathematica

Table[PrimeNu[n]-PrimeNu[EulerPhi[n]], {n, 90}] (* Harvey P. Dale, Mar 03 2016 *)

Prog

(PARI) for(n=1, 50, print1(omega(n) - omega(eulerphi(n)), ", ")) \\ G. C. Greubel, May 19 2017

Crossrefs

Cf. A000010, A001221.

Sequence in context: A032337 A380955 A058190 * A006997 A141612 A316342

Adjacent sequences: A055733 A055734 A055735 * A055737 A055738 A055739

Keyword

sign

Author

Labos Elemer, Jul 11 2000

Status

approved