A181837 - OEIS

%I #10 Dec 03 2023 07:06:40

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,

%T 0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,

%U 0,1,1,0,1,1,1,1,0,0,0,0,0,0

%N T(n,k) = [k is strongly prime to n], the indicator function of strong coprimality, triangle read by rows.

%C k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.

%C T(n,k) = [k is strong prime to n] where [] denotes the Iverson bracket.

%H Peter Luschny, <a href="http://www.oeis.org/wiki/User:Peter_Luschny/StrongCoprimality">Strong coprimality</a>.

%e [n=0]          0

%e [n=1]         0, 0

%e [n=2]       0, 0, 0

%e [n=3]      0, 0, 0, 0

%e [n=4]    0, 0, 0, 0, 0

%e [n=5]   0, 0, 0, 1, 0, 0

%e Let n = 5 then the numbers prime to n are {1, 2, 3, 4} and the positive divisors of n-1 are {1, 2, 4}. Thus only 3 is strong prime to 5.

%o (SageMath)

%o def isstrongprimeto(k, n): return not(k.divides(n - 1)) and gcd(k, n) == 1

%o for n in srange(12): print([int(isstrongprimeto(k, n)) for k in srange(n+1)])

%o # _Peter Luschny_, Dec 03 2023

%Y Cf. A181830, A181831, A181832, A181838, A054431.

%K nonn,tabl

%O 0

%A _Peter Luschny_, Nov 17 2010

%E Corrected T(1, 1) to 0 by _Peter Luschny_, Dec 03 2023