A070777 a(1) = 1; a(n) = (largest prime factor of n) - 1.

1, 1, 2, 1, 4, 2, 6, 1, 2, 4, 10, 2, 12, 6, 4, 1, 16, 2, 18, 4, 6, 10, 22, 2, 4, 12, 2, 6, 28, 4, 30, 1, 10, 16, 6, 2, 36, 18, 12, 4, 40, 6, 42, 10, 4, 22, 46, 2, 6, 4, 16, 12, 52, 2, 10, 6, 18, 28, 58, 4, 60, 30, 6, 1, 12, 10, 66, 16, 22, 6, 70, 2, 72, 36, 4, 18, 10, 12, 78, 4, 2, 40, 82, 6

Offset: 1

Author

Labos Elemer, May 07 2002

Keywords

• easy
• nonn

Comments

Also a(n) = Euler Phi of largest prime factor of n (previous name).

a(m*n) = max(a(m), a(n)). - Robert Israel, May 19 2015

Examples

			102 = 2*3*17, so a(102) = 17 - 1 = 16.
		

Crossrefs

Cf. A000010, A006530, A068211, A070812.

Programs

Maple

with(numtheory): A070777 := n -> `if`(n=1,1,phi(max(op(factorset(n))))): # Peter Luschny, Oct 23 2010

Mathematica

a[n_] := EulerPhi[Last[FactorInteger[n]][[1]]]; Table[a[n], {n, 1, 200}] (* José María Grau Ribas, Feb 21 2010 *)

PARI

a(n) = if (n==1, 1, vecmax(factor(n)[,1]) - 1); \\ after A006530; Michel Marcus, May 19 2015

Formula

a(n) = A000010(A006530(n)) = A006530(n) - 1 if n >= 2.

Extensions

New name from Michel Marcus, May 19 2015