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%I #6 Feb 20 2022 14:36:17
%S 2,2,1,2,0,3,2,1,0,4,2,0,0,0,9,2,1,3,0,0,7,2,0,0,0,0,0,15,2,1,0,4,0,0,
%T 0,12,2,0,3,0,0,0,0,0,18,2,1,0,0,9,0,0,0,0,17
%N Triangle, A007444(k) in each column interspersed with k zeros.
%C Row sums = the primes. T(n,k) = 0 if k does not divide n. If k divides n, extract A007444(k) which become the nonzero terms of row n, sum = n-th prime. Example: The factors of 6 are (1, 2, 3 and 6) = k's for A007444(k) = (2 + 1 + 3 + 7) = p(6) = 13. A007444 = the Moebius transform of the primes, (2, 1, 3, 4, 9, 7, 15, 12, ...), as the right diagonal of A130071.
%F Given the Moebius transform of the primes, A007444: (2, 1, 3, 4, 9, 7, 15, ...), the k-th term (k= 1,2,3,...) of this sequence generates the k-th column of A130071, interspersed with (k-1) zeros.
%e First few rows of the triangle:
%e 2;
%e 2, 1;
%e 2, 0, 3;
%e 2, 1, 0, 4;
%e 2, 0, 0, 0, 9;
%e 2, 1, 3, 0, 0, 7;
%e 2, 0, 0, 0, 0, 0, 15;
%e 2, 1, 0, 4, 0, 0, 0, 12;
%e 2, 0, 3, 0, 0, 0, 0, 0, 18;
%e 2, 1, 0, 0, 9, 0, 0, 0, 0, 17;
%e ...
%Y Cf. A130070, A007444, A054525, A000040.
%K nonn,tabl
%O 1,1
%A _Gary W. Adamson_, May 05 2007
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