

A130071


Triangle, A007444(k) in each column interspersed with k zeros.


2



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, 0, 12, 2, 0, 3, 0, 0, 0, 0, 0, 18, 2, 1, 0, 0, 9, 0, 0, 0, 0, 17
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OFFSET

1,1


COMMENTS

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 = nth 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.


LINKS

Table of n, a(n) for n=1..55.


FORMULA

Given the Moebius transform of the primes, A007444: (2, 1, 3, 4, 9, 7, 15,...), the kth term (k= 1,2,3,...) of this sequence generates the kth column of A130071, interspersed with (k1) zeros.


EXAMPLE

First few rows of the triangle are:
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, 0, 12;
2, 0, 3, 0, 0, 0, 0, 0, 18;
2, 1, 0, 0, 9, 0, 0, 0, 0, 17;
...


CROSSREFS

Cf. A130070, A007444, A054525, A000040.
Sequence in context: A089077 A203398 A225064 * A321373 A305615 A038540
Adjacent sequences: A130068 A130069 A130070 * A130072 A130073 A130074


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, May 05 2007


STATUS

approved



