cp's OEIS Frontend

A198067 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.

%I A198067 #9 Apr 20 2013 03:42:37
%S A198067 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 A198067 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 A198067 2,2,1,2,1,1,1,1,1,1,7,1,6,2,3,1,3,1,2
%N A198067 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 A198067 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 A198067 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/EulerTotient">Euler's totient function</a>
%e A198067 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 A198067 -
%e A198067 [x][1][2][3][4][5][6][7][8]
%e A198067 [1] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 [2] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 [3] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 [4] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 [5] 2, 2, 2, 1, 2, 2, 2, 1
%e A198067 [6] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 [7] 3, 3, 3, 2, 3, 2, 3, 2
%e A198067 [8] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 -
%e A198067 Triangle k=1..n, n>=1:
%e A198067 [1]           1
%e A198067 [2]          1, 1
%e A198067 [3]        1, 1, 1
%e A198067 [4]       1, 1, 1, 1
%e A198067 [5]     2, 2, 2, 1, 2
%e A198067 [6]    1, 1, 1, 1, 1, 1
%e A198067 [7]  3, 3, 3, 2, 3, 2, 3
%e A198067 [8] 1, 1, 1, 1, 1, 1, 1, 1
%e A198067 -
%e A198067 Triangle n=1..k, k>=1:
%e A198067 [1]           1
%e A198067 [2]          1, 1
%e A198067 [3]        1, 1, 1
%e A198067 [4]       1, 1, 1, 1
%e A198067 [5]     1, 1, 1, 1, 2
%e A198067 [6]    1, 1, 1, 1, 2, 1
%e A198067 [7]  1, 1, 1, 1, 2, 1, 3
%e A198067 [8] 1, 1, 1, 1, 1, 1, 2, 1
%p A198067 strongdivisors := n -> numtheory[divisors](n) minus {1}:
%p A198067 coprimes  := n -> select(k->igcd(k, n)=1, {$1..n}):
%p A198067 nonprimes := n -> remove(isprime, {$1..n});
%p A198067 T := (n,k) -> nops(nonprimes(n) intersect (coprimes(n) minus strongdivisors(k))):
%p A198067 seq(seq(T(n-k+1, k), k=1..n), n=1..13);  # Square array by antidiagonals.
%p A198067 seq(print(seq(T(n,k), k=1..n)), n=1..8); # Lower triangle.
%p A198067 seq(print(seq(T(n,k), n=1..k)), k=1..8); # Upper triangle.
%Y A198067 Cf. A000010, A048864, A193804, A193805, A198066.
%K A198067 nonn,tabl
%O A198067 1,11
%A A198067 _Peter Luschny_, Nov 07 2011