A097946 a(n) = A008683(n)*A014197(n) where A008683 is the Moebius (or Mobius) function mu(n) and A014197 is the number of numbers m with Euler phi(m) = n.

2, -3, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Gerald McGarvey, Sep 04 2004

Keywords

• sign

Comments

For n < 93 and a(n) not 0, n = p - 1 where p is prime and therefore in A077064 (Squarefree numbers of form prime - 1.)

Links

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

Crossrefs

Cf. A000010, A008683, A014197, A077064, A097945.

Programs

PARI

A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))} \\ This function from M. F. Hasler, Oct 05 2009
A097946(n) = moebius(n)*A014197(n); \\ Antti Karttunen, Jul 19 2017