OFFSET
1,8
COMMENTS
LINKS
Anonymous?, Polynomial calculator
Eric Weisstein's World of Mathematics, Roundness
G. Xiao, WIMS server, Factoris (both expands and factors polynomials)
FORMULA
If A025487(n)'s canonical factorization into prime powers is the product of p^e(p), then T(n, m) is the coefficient of k^m in the polynomial expansion of Product_p (sum_{i=0..e} k^i).
EXAMPLE
Rows begin:
1;
1,1;
1,1,1;
1,2,1;
1,1,1,1;
1,2,2,1;
1,1,1,1,1;...
36's 9 divisors include 1 divisor with 0 total prime factors (1);, 2 with 1 (2 and 3); 3 with 2 (4, 6 and 9); 2 with 3 (12 and 18); and 1 with 4 (36). Since 36 = A025487(11), the 11th row of the table therefore reads (1, 2, 3, 2, 1). These are the positive coefficients of the polynomial 1 + 2k + 3k^2 + 2k^3 + (1)k^4 = (1 + k + k^2)(1 + k + k^2), derived from the prime factorization of 36 (namely, 2^2*3^2).
CROSSREFS
For the number of prime factors of n counted with multiplicity, see A001222.
KEYWORD
nonn,tabf
AUTHOR
Matthew Vandermast, Nov 11 2008
STATUS
approved