A160598 Numerator of coresilience C(n) = (n - phi(n))/(n-1).

1, 1, 2, 1, 4, 1, 4, 3, 2, 1, 8, 1, 8, 1, 8, 1, 12, 1, 12, 9, 4, 1, 16, 5, 14, 9, 16, 1, 22, 1, 16, 13, 6, 11, 24, 1, 20, 15, 8, 1, 30, 1, 24, 21, 8, 1, 32, 7, 30, 19, 28, 1, 36, 5, 32, 3, 10, 1, 44, 1, 32, 27, 32, 17, 46, 1, 36, 25, 2, 1, 48, 1, 38, 35, 8, 17, 54, 1, 48, 27, 14, 1, 60, 1

Offset: 2

Author

M. F. Hasler, May 23 2009

Keywords

• nonn
• frac

Comments

Obviously C(p) = 1/(p-1), i.e., a(p)=1, for all primes p. Sequence A160599 lists composite numbers for which this is the case.

Examples

			a(10)=2 since for n=10, we have (n - phi(n))/(n-1) = (10-4)/9 = 2/3.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..10000
• Project Euler, Problem 245: resilient fractions, May 2009

Crossrefs

Cf. A160595, A160596, A160597, A160599.

Programs

Magma

[Numerator((n-EulerPhi(n))/(n-1)): n in [2..80]]; // Vincenzo Librandi, Dec 27 2016

Mathematica

Numerator[Table[(n - EulerPhi[n])/(n - 1), {n, 2, 90}]] (* Vincenzo Librandi, Dec 27 2016 *)

PARI

A160598(n)=numerator((n-eulerphi(n))/(n-1))