OFFSET
0,8
COMMENTS
k is strongly prime to n if and only if k is relatively prime to n and k does not divide n - 1.
It is conjectured (see Scroggs link) that a(n) is also the number of cardboard braids that work with n slots. - Matthew Scroggs, Sep 23 2017
a(n) is odd if and only if n is in A002522 but n <> 2. - Robert Israel, Jun 20 2018
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Peter Luschny, Strong coprimality
Matthew Scroggs, Braiding, pt. 2. Two results and a conjecture
EXAMPLE
a(11) = card({1,2,3,4,5,6,7,8,9,10} - {1,2,5,10}) = card({3,4,6,7,8,9}) = 6.
MATHEMATICA
a[0]=0; a[1]=0; a[n_ /; n > 1] := Select[Range[n], CoprimeQ[#, n] && !Divisible[n-1, #] &] // Length; Table[a[n], {n, 0, 66}] (* Jean-François Alcover, Jun 26 2013 *)
PROG
(PARI) a(n)=if(n<2, 0, eulerphi(n)-numdiv(n-1));
for (i=0, 66, print1(a(i), ", ")) \\ Michel Marcus, May 22 2017
(SageMath)
def isstrongprimeto(k, n): return not(k.divides(n - 1)) and gcd(k, n) == 1
print([sum(int(isstrongprimeto(k, n)) for k in srange(n+1)) for n in srange(67)])
# Peter Luschny, Dec 03 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Nov 17 2010
EXTENSIONS
Corrected a(1) to 0 by Peter Luschny, Dec 03 2023
STATUS
approved