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%I #9 Apr 20 2013 03:42:37
%S 1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,3,1,2,1,1,1,1,1,3,1,1,1,1,
%T 1,1,3,1,3,1,2,1,1,1,1,2,3,1,2,1,2,1,1,1,1,6,2,3,1,3,1,2,1,1,1,1,1,6,
%U 2,2,1,2,1,1,1,1,1,1,7,1,6,2,3,1,3,1,2
%N Square array read by antidiagonals, n>=1, k>=1; T(n,k) is the number of nonprime numbers which are prime to n and are not strong divisors of k.
%C We say d is a strong divisor of n iff d is a divisor of n and d > 1. Let alpha(n) be number of nonprime numbers in the reduced residue system of n. Then alpha(n) = T(n,1) = T(n,n).
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/EulerTotient">Euler's totient function</a>
%e T(15, 22) = card({1,4,8,14}) = 4 because the coprimes of 15 are {1,2,4,7,8,11,13,14} and the strong divisors of 22 are {2,11,22}.
%e -
%e [x][1][2][3][4][5][6][7][8]
%e [1] 1, 1, 1, 1, 1, 1, 1, 1
%e [2] 1, 1, 1, 1, 1, 1, 1, 1
%e [3] 1, 1, 1, 1, 1, 1, 1, 1
%e [4] 1, 1, 1, 1, 1, 1, 1, 1
%e [5] 2, 2, 2, 1, 2, 2, 2, 1
%e [6] 1, 1, 1, 1, 1, 1, 1, 1
%e [7] 3, 3, 3, 2, 3, 2, 3, 2
%e [8] 1, 1, 1, 1, 1, 1, 1, 1
%e -
%e Triangle k=1..n, n>=1:
%e [1] 1
%e [2] 1, 1
%e [3] 1, 1, 1
%e [4] 1, 1, 1, 1
%e [5] 2, 2, 2, 1, 2
%e [6] 1, 1, 1, 1, 1, 1
%e [7] 3, 3, 3, 2, 3, 2, 3
%e [8] 1, 1, 1, 1, 1, 1, 1, 1
%e -
%e Triangle n=1..k, k>=1:
%e [1] 1
%e [2] 1, 1
%e [3] 1, 1, 1
%e [4] 1, 1, 1, 1
%e [5] 1, 1, 1, 1, 2
%e [6] 1, 1, 1, 1, 2, 1
%e [7] 1, 1, 1, 1, 2, 1, 3
%e [8] 1, 1, 1, 1, 1, 1, 2, 1
%p strongdivisors := n -> numtheory[divisors](n) minus {1}:
%p coprimes := n -> select(k->igcd(k, n)=1, {$1..n}):
%p nonprimes := n -> remove(isprime, {$1..n});
%p T := (n,k) -> nops(nonprimes(n) intersect (coprimes(n) minus strongdivisors(k))):
%p seq(seq(T(n-k+1, k), k=1..n), n=1..13); # Square array by antidiagonals.
%p seq(print(seq(T(n,k), k=1..n)), n=1..8); # Lower triangle.
%p seq(print(seq(T(n,k), n=1..k)), k=1..8); # Upper triangle.
%Y Cf. A000010, A048864, A193804, A193805, A198066.
%K nonn,tabl
%O 1,11
%A _Peter Luschny_, Nov 07 2011
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