1,12

All rows are palindromic. (n,0)=(n, A001222(n))=1.

Two numbers have identical rows in the table if and only if they have the same prime signature.

Anonymous?, Polynomial calculator

Eric Weisstein's World of Mathematics, Roundness

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

If the canonical factorization of n 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; 1,1,1; 1,1; 1,2,1; 1,1; 1,1,1,1; 1,1,1; 1,2,1;...

12 has 1 divisor with 0 total prime factors (1), 2 with 1 (2 and 3), 2 with 2 (4 and 6) and 1 with 3 (12), for a total of 6. The 12th row of the table therefore reads (1, 2, 2, 1). These are the positive coefficients of the polynomial 1 + 2k + 2k^2 + (1)k^3 = (1 + k + k^2)(1 + k), derived from the prime factorization of 12 (namely, 2^2*3^1).

Row sums equal A000005(n). (n, 1)= A001221(n) for n>1.

Row n of A007318 is identical to row A002110(n) of this table and also identical to the row for any squarefree number with n prime factors.

Cf. A146292. Also cf. A146289, A146290.

Sequence in context: A043287 A043286 A043285 this_sequence A086251 A092931 A147300

Adjacent sequences: A146288 A146289 A146290 this_sequence A146292 A146293 A146294

nonn,tabf

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