A181837 T(n,k) = [k is strongly prime to n], the indicator function of strong coprimality, triangle read by rows.

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, 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, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0

Offset

0

Comments

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

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

Links

Table of n, a(n) for n=0..81.

Peter Luschny, Strong coprimality.

Example

[n=0]          0
[n=1]         0, 0
[n=2]       0, 0, 0
[n=3]      0, 0, 0, 0
[n=4]    0, 0, 0, 0, 0
[n=5]   0, 0, 0, 1, 0, 0
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.

Prog

(SageMath)
def isstrongprimeto(k, n): return not(k.divides(n - 1)) and gcd(k, n) == 1
for n in srange(12): print([int(isstrongprimeto(k, n)) for k in srange(n+1)])
# Peter Luschny, Dec 03 2023

Crossrefs

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

Sequence in context: A304570 A304571 A181838 * A185709 A011732 A353473

Adjacent sequences: A181834 A181835 A181836 * A181838 A181839 A181840

Keyword

nonn,tabl

Author

Peter Luschny, Nov 17 2010

Extensions

Corrected T(1, 1) to 0 by Peter Luschny, Dec 03 2023

Status

approved