A339872 Index k of the least prime(k) such that prime(k)-adic valuation of phi(n) exceeds the prime(k)-adic valuation of n-1, or 0 if no such k exists (for example, when n = 1 or a prime).

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

Offset: 1

Author

Antti Karttunen, Dec 20 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A055396, A160595, A339817, A339871.

Programs

PARI

A339872(n) = if(1==n,0,for(k=1,n,my(p=prime(k)); if(valuation(eulerphi(n),p)>valuation(n-1,p), return(k))); (0));

PARI

A339872(n) = if(1==n,0,my(f=factor(eulerphi(n))); for(i=1,#f~,if(f[i,2]>valuation(n-1,f[i,1]), return(primepi(f[i,1])))); (0));

PARI

A339872(n) = { my(t=eulerphi(n), x=t/gcd(n-1,t)); if(1==x,0,primepi(factor(x)[1, 1])); };

Formula

a(n) = A055396(A160595(n)).