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A138948
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Triangle T[i,j] = exponent of prime A000040(j) in factorization of composite A002808(i).
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1
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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
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1,1
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COMMENTS
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This is the lower left half of A063173 (whose upper right half is zero), see there for more information and cross-references.
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LINKS
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Table of n, a(n) for n=1..105.
N. Fernandez, The prime-composite array, B(m,n) and the Borve conjectures.
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FORMULA
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A002808(i) = product( A000040(j)^T[i,j], j=1..i), where T[i,j] = a(i(i-1)/2+j)
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EXAMPLE
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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.
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PROG
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(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])))
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CROSSREFS
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Cf. A063173.
Sequence in context: A082386 A028306 A111259 * A186114 A155726 A105400
Adjacent sequences: A138945 A138946 A138947 * A138949 A138950 A138951
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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M. F. Hasler, Apr 27 2008
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STATUS
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approved
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