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A138948 Triangle T[i,j] = exponent of prime A000040(j) in factorization of composite A002808(i). 1

%I

%S 2,1,1,3,0,0,0,2,0,0,1,0,1,0,0,2,1,0,0,0,0,1,0,0,1,0,0,0,0,1,1,0,0,0,

%T 0,0,4,0,0,0,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,2,0,1,0,0,0,0,0,0,0,0,0,1,

%U 0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,3,1,0,0,0,0,0,0,0,0,0,0,0,0

%N Triangle T[i,j] = exponent of prime A000040(j) in factorization of composite A002808(i).

%C This is the lower left half of A063173 (whose upper right half is zero), see there for more information and cross-references.

%H N. Fernandez, <a href="http://www.borve.org/primeness/pcarray.html">The prime-composite array, B(m,n) and the Borve conjectures</a>.

%F A002808(i) = product( A000040(j)^T[i,j], j=1..i), where T[i,j] = a(i(i-1)/2+j)

%e The first row (2) of the triangle corresponds to the first composite number A002808(1) = 4 = 2^2 = prime(1)^2.

%e The 2nd row (1,1) of the triangle corresponds to the 2nd composite number A002808(2) = 6 = 2^1 * 3^1 = A000040(1)^1 A000040(2)^1.

%e The 3rd row (3,0,0) of the triangle corresponds to the 3rd composite number A002808(3) = 8 = 2^3 = A000040(1)^3 A000040(2)^0 A000040(3)^0.

%o (PARI) T=matrix(40,40,i,j,t=0;until(c[i]%prime(j)^t++,);t-1); A138948=concat(vector(vecmin(matsize(T)),i,vector(i,j,T[i,j])))

%Y Cf. A063173.

%K easy,nonn,tabl

%O 1,1

%A _M. F. Hasler_, Apr 27 2008

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Last modified September 22 12:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)