A322019 a(n) = A000005(n) - A014197(n), where A000005(n) gives the number of divisors of n, and A014197(n) gives the number of integers m with phi(m) = n.

-1, -1, 2, -1, 2, 0, 2, -1, 3, 2, 2, 0, 2, 4, 4, -1, 2, 2, 2, 1, 4, 2, 2, -2, 3, 4, 4, 4, 2, 6, 2, -1, 4, 4, 4, 1, 2, 4, 4, -1, 2, 4, 2, 3, 6, 2, 2, -1, 3, 6, 4, 4, 2, 6, 4, 5, 4, 2, 2, 3, 2, 4, 6, -1, 4, 6, 2, 6, 4, 6, 2, -5, 2, 4, 6, 6, 4, 6, 2, 0, 5, 2, 2, 6, 4, 4, 4, 2, 2, 12, 4, 3, 4, 4, 4, -5, 2, 6, 6, 5, 2, 6, 2, 5, 8

Offset: 1

Author

Antti Karttunen, Dec 03 2018

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20790
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A000005, A014197, A305058 (positions of zeros).

Cf. also A305896.

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))))}; \\ From A014197
A322019(n) = (numdiv(n)-A014197(n));

Formula

a(n) = A000005(n) - A014197(n).