

A138948


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


1



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, 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, 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
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OFFSET

1,1


COMMENTS

This is the lower left half of A063173 (whose upper right half is zero), see there for more information and crossreferences.


LINKS

Table of n, a(n) for n=1..105.
N. Fernandez, The primecomposite array, B(m,n) and the Borve conjectures.


FORMULA

A002808(i) = product( A000040(j)^T[i,j], j=1..i), where T[i,j] = a(i(i1)/2+j)


EXAMPLE

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


PROG

(PARI) T=matrix(40, 40, i, j, t=0; until(c[i]%prime(j)^t++, ); t1); A138948=concat(vector(vecmin(matsize(T)), i, vector(i, j, T[i, j])))


CROSSREFS

Cf. A063173.
Sequence in context: A111259 A304195 A320076 * A186114 A326934 A290691
Adjacent sequences: A138945 A138946 A138947 * A138949 A138950 A138951


KEYWORD

easy,nonn,tabl


AUTHOR

M. F. Hasler, Apr 27 2008


STATUS

approved



