A181838 T(n,p) = [p prime and is strongly prime to n], the indicator function of strongly coprime primes, 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, 0, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 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,p) = p is prime and [p is strong prime to n], [] denotes the Iverson bracket.

Links

Table of n, a(n) for n=0..126.

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
[n=6]   0, 0, 0, 0, 0, 0, 0
[n=7]  0, 0, 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 the prime 3 is strong prime to 5.

Maple

A181838_triangle := proc(M)
local Primes, strongCoprimes, strongCoprimePrimes, triangle;
Primes := n -> select(k->isprime(k), {$1..n}):
strongCoprimes := n -> select(k->igcd(k, n)=1, {$1..n})
minus numtheory[divisors](n-1):
strongCoprimePrimes := n -> Primes(n) intersect strongCoprimes(n):
triangle := proc(N, C) local T, L, k, n;
for n from 0 to N do
  T := C(n); L := NULL;
  for k from 0 to n do
    L := L, `if`(member(k, T), 1, 0)
  od;
  print(L)
od end:
triangle(M, strongCoprimePrimes) end:

Mathematica

strongCoprimeQ[k_, n_] := PrimeQ[k] && CoprimeQ[n, k] && !Divisible[n-1, k]; Table[Boole[strongCoprimeQ[k, n]], {n, 0, 15}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 19 2013 *)

Crossrefs

Cf. A181830, A181831, A181832, A181837, A054431.

Sequence in context: A297045 A304570 A304571 * A181837 A185709 A011732

Adjacent sequences: A181835 A181836 A181837 * A181839 A181840 A181841

Keyword

nonn,tabl

Author

Peter Luschny, Nov 17 2010

Extensions

Keyword tabl by Michel Marcus, Apr 08 2013

Status

approved