OFFSET
1,4
COMMENTS
Does every natural number appear in this sequence? If so, do they appear infinitely many times? - Eric Chen, Nov 26 2014
Number n is (Fermat) pseudoprimes (or prime) to one in a(n) of its coprime bases. That is, b^(n-1) = 1 (mod n) for one in a(n) of numbers b coprime to n. - Eric Chen, Nov 26 2014
a(n) = 1 if and only if n is 1, prime (A000040), or Carmichael number (A002997). - Eric Chen, Nov 26 2014
a(p^n) = p^(n-1), where p is a prime. - Eric Chen, Nov 26 2014
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
GĂ©rard P. Michon, Pseudoprimes
FORMULA
A003557(n) <= a(n) <= n, and a(n) is a multiple of A003557(n). - Charles R Greathouse IV, Nov 17 2014
EXAMPLE
EulerPhi(15) = 8, and that 15 is a Fermat pseudoprime in base 1, 4, 11, and 14, the total is 4 bases, so a(15) = 8/4 = 2.
MATHEMATICA
a063994[n_] := Times @@ GCD[n - 1, First /@ FactorInteger@ n - 1]; a063994[1] = 1; a247074[n_] := EulerPhi[n]/a063994[n]; Array[a247074, 150]
PROG
(PARI) a(n)=my(f=factor(n)); eulerphi(f)/prod(i=1, #f~, gcd(f[i, 1]-1, n-1)) \\ Charles R Greathouse IV, Nov 17 2014
CROSSREFS
KEYWORD
AUTHOR
Eric Chen, Nov 16 2014
STATUS
approved