A143614 - OEIS

%I #6 May 29 2023 13:01:33

%S 1,1,0,2,1,0,2,0,1,0,4,2,1,1,0,2,0,0,0,1,0,6,3,2,1,1,1,0,4,0,1,0,1,0,

%T 1,0,6,3,0,2,1,0,1,1,0,4,0,2,0,0,0,1,0,1,0,10,5,3,2,2,1,1,1,1,1,0,4,0,

%U 0,0,1,0,1,0,0,0,1,0,12,6,4,3,2,2,1,1,1,1,1,1,0,6,0,2,0,1,0,0,0,1,0,1,0,1,0

%N Triangle read by rows: A054521 * A051731 as infinite lower triangular matrices.

%C Left border = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6,...).

%C Row sums = A143615: (1, 1, 3, 3, 8, 3, 14, 7,...).

%F A054521 records the relative primes of n, indicated by a 1's in row n, 0 otherwise. A051731 = the inverse Moebius transform, in which 1's by rows indicate the divisors of n, 0 otherwise.

%e First few rows of the triangle =

%e 1;

%e 1, 0;

%e 2, 1, 0;

%e 2, 0, 1, 0;

%e 4, 2, 1, 1, 0;

%e 2, 0, 0, 0, 1, 0;

%e 6, 3, 2, 1, 1, 1, 0;

%e 4, 0, 1, 0, 1, 0, 1, 0;

%e 6, 3, 0, 2, 1, 0, 1, 1, 0;

%e ...

%Y Cf. A000010, A051731, A054521, A143615.

%K nonn,tabl

%O 1,4

%A _Gary W. Adamson_, Aug 27 2008

%E a(96) and a(101) split by _Georg Fischer_, May 29 2023