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 A198068 Square array read by antidiagonals, n>=1, k>=1; T(n,k) is the number of primes which are prime to n and are not strong divisors of k. 0
 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 2, 2, 1, 0, 1, 2, 2, 1, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 0, 2, 2, 2, 2, 3, 3, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 1, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS We say d is a strong divisor of n iff d is a divisor of n and d > 1. Let omega(n) be the number of distinct primes dividing n. Then omega(n) = T(n,1) = T(n,n). LINKS Peter Luschny, Euler's totient function EXAMPLE T(15, 22) = card({2,3,5,11}) = 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}. - [x][1][2][3][4][5][6][7][8] [1] 0, 0, 0, 0, 0, 0, 0, 0 [2] 1, 1, 1, 1, 1, 1, 1, 1 [3] 1, 2, 1, 2, 1, 2, 1, 2 [4] 1, 1, 2, 1, 1, 2, 1, 1 [5] 1, 2, 2, 2, 1, 3, 1, 2 [6] 2, 2, 2, 2, 3, 2, 2, 2 [7] 1, 2, 2, 2, 2, 3, 1, 2 [8] 1, 1, 2, 1, 2, 2, 2, 1 - Triangle k=1..n, n>=1: [1]           0 [2]          1, 1 [3]        1, 2, 1 [4]       1, 1, 2, 1 [5]     1, 2, 2, 2, 1 [6]    2, 2, 2, 2, 3, 2 [7]  1, 2, 2, 2, 2, 3, 1 [8] 1, 1, 2, 1, 2, 2, 2, 1 - Triangle n=1..k, k>=1: [1]           0 [2]          0, 1 [3]        0, 1, 1 [4]       0, 1, 2, 1 [5]     0, 1, 1, 1, 1 [6]    0, 1, 2, 2, 3, 2 [7]  0, 1, 1, 1, 1, 2, 1 [8] 0, 1, 2, 1, 2, 2, 2, 1 MAPLE strongdivisors := n -> numtheory[divisors](n) minus {1}: coprimes  := n -> select(k->igcd(k, n)=1, {\$1..n}): primes := n -> select(isprime, {\$1..n}); T := (n, k) -> nops(primes(n) intersect ({\$1..n} minus (coprimes(n) minus strongdivisors(k)))): seq(seq(T(n-k+1, k), k=1..n), n=1..13);  # Square array by antidiagonals. seq(print(seq(T(n, k), k=1..n)), n=1..8); # Lower triangle. seq(print(seq(T(n, k), n=1..k)), k=1..8); # Upper triangle. CROSSREFS Cf. A000010, A001221, A193804, A193805, A198066, A198067. Sequence in context: A106799 A212210 A127499 * A121361 A191907 A052343 Adjacent sequences:  A198065 A198066 A198067 * A198069 A198070 A198071 KEYWORD nonn,tabl AUTHOR Peter Luschny, Nov 08 2011 STATUS approved

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