A339872 - OEIS

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

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OFFSET

1,9

LINKS

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

FORMULA

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

PROG

(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])); };

CROSSREFS