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A104244
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Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then we can define Pn(x) = e1 + (e2)*x + (e3)*(x^2) + (e4)*(x^3) + ... + (ek)*(x^(k-1)) + ... The sequence is the table T(n,x)=Pn(x) read by antidiagonals. A090883 is the main diagonal of this table.
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1
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0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 1, 2, 3, 1, 0, 2, 4, 2, 4, 1, 0, 1, 3, 9, 2, 5, 1, 0, 3, 8, 4, 16, 2, 6, 1, 0, 2, 3, 27, 5, 25, 2, 7, 1, 0, 2, 4, 3, 64, 6, 36, 2, 8, 1, 0, 1, 5, 6, 3, 125, 7, 49, 2, 9, 1, 0, 3, 16, 10, 8, 3, 216, 8, 64, 2, 10, 1, 0, 1, 4, 81, 17, 10, 3, 343, 9, 81, 2, 11, 1, 0, 2, 32, 5
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