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

1,14

Links

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

Formula

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

a(n) <= A055734(n).

Prog

(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)));

Crossrefs

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

Sequence in context: A143439 A105469 A257857 * A276806 A308427 A378662

Adjacent sequences: A339868 A339869 A339870 * A339872 A339873 A339874

Keyword

nonn

Author

Antti Karttunen, Dec 20 2020

Status

approved