A339871 Number of primes p for which the p-adic valuation of phi(n) exceeds the p-adic valuation of n-1, with a(1) = 0 by convention.

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 2, 1, 2, 0, 1, 0, 3, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 1, 2, 0, 2, 1, 3, 2, 2, 0, 2, 1, 2, 2, 2, 2, 1, 0, 3, 3, 2, 0, 1, 0, 2, 2

Offset: 1

Author

Antti Karttunen, Dec 20 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A001221, A055734, A160595, A339817, A339872.

Programs

PARI

A339871(n) = if(1==n,0,my(s=0); for(k=1,n,my(p=prime(k)); if(valuation(eulerphi(n),p)>valuation(n-1,p), s++)); (s));

PARI

A339871(n) = if(1==n,0,my(f=factor(eulerphi(n))); sum(i=1,#f~,f[i,2]>valuation(n-1,f[i,1])));

PARI

A339871(n) = omega(eulerphi(n)/gcd(n-1,eulerphi(n)));

Formula

a(n) = A001221(A160595(n)).

a(n) <= A055734(n).