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%I #16 Dec 19 2013 05:38:55
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%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 0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0
%N T(n,p) = [p prime and is strongly prime to n], the indicator function of strongly coprime primes, 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,p) = p is prime and [p is strong prime to n], [] 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 [n=6] 0, 0, 0, 0, 0, 0, 0
%e [n=7] 0, 0, 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 the prime 3 is strong prime to 5.
%p A181838_triangle := proc(M)
%p local Primes, strongCoprimes, strongCoprimePrimes, triangle;
%p Primes := n -> select(k->isprime(k),{$1..n}):
%p strongCoprimes := n -> select(k->igcd(k,n)=1,{$1..n})
%p minus numtheory[divisors](n-1):
%p strongCoprimePrimes := n -> Primes(n) intersect strongCoprimes(n):
%p triangle := proc(N, C) local T, L, k, n;
%p for n from 0 to N do
%p T := C(n); L := NULL;
%p for k from 0 to n do
%p L := L, `if`(member(k,T),1,0)
%p od;
%p print(L)
%p od end:
%p triangle(M, strongCoprimePrimes) end:
%t 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 *)
%Y Cf. A181830, A181831, A181832, A181837, A054431.
%K nonn,tabl
%O 0
%A _Peter Luschny_, Nov 17 2010
%E Keyword tabl by _Michel Marcus_, Apr 08 2013
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