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

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..105.

N. Fernandez, The prime-composite 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(i-1)/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++, ); t-1); 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