1,8

All rows are palindromic. (n, 0) = (n, (A036041(n)) = 1.

Every row that appears in A146291 appears exactly once in the table. Rows appear in order of first appearance in A146291.

Anonymous?, Polynomial calculator

Eric Weisstein's World of Mathematics, Roundness

G. Xiao, WIMS server, Factoris (both expands and factors polynomials)

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).

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).

For the number of prime factors of n counted with multiplicity, see A001222.

Row sums equal A146288(n). (n, 1) = A061394(n) for n>1.

Row A098719(n) of this table is identical to row n of A007318.

Cf. A146291. Also cf. A146289, A146290.

Sequence in context: A085021 A060209 A037830 this_sequence A139039 A122172 A025910

Adjacent sequences: A146289 A146290 A146291 this_sequence A146293 A146294 A146295

nonn,tabf

Matthew Vandermast (ghodges14(AT)comcast.net), Nov 11 2008