|
| |
|
|
A108455
|
|
Table read by antidiagonals: T(n,k) = number of factorizations of (n,k) into pairs (i,j) with i>0, j>0 (and if i=1 then j=1).
|
|
3
| |
|
|
1, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 3, 1, 3, 1, 0, 1, 1, 2, 1, 3, 1, 2, 0, 1, 1, 3, 1, 4, 1, 3, 2, 0, 1, 1, 2, 1, 3, 1, 3, 2, 2, 0, 1, 1, 3, 1, 5, 1, 4, 2, 3, 1, 0, 1, 1, 3, 1, 3, 1, 3, 3, 3, 1, 3, 0, 1, 1, 3, 1, 5, 1, 5, 2, 4, 1, 5, 1, 0, 1, 1, 2, 1, 4, 1, 3, 3, 3, 1, 5, 1, 2
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,10
|
|
|
COMMENTS
| (a,b)*(x,y)=(a*x,b*y); unit is (1,1).
|
|
|
FORMULA
| For n>1, T(n,m)=ceiling((tau(n)-2)*tau(m)/2)+1, where tau(n) = A000005(n). - Franklin T. Adams-Watters (FrankTAW(AT)netscape.net), Jun 23 2010.
Dirichlet g.f.: A(s, t) = exp(B(s, t)/1 + B(2*s, 2*t)/2 + B(3*s, 3*t)/3 + ...) where B(s, t) = zeta(s)*(zeta(t)-1).
|
|
|
EXAMPLE
| 1 0 0 0 0 ...
1 1 1 1 1 ...
1 1 1 1 1 ...
2 2 2 3 2 ...
1 1 1 1 1 ...
(6,4)=(3,4)*(2,1)=(3,1)*(2,4)=(3,2)*(2,2), so a(6,4)=4.
|
|
|
MATHEMATICA
| rows = 14; t[n_, m_] := Ceiling[(DivisorSigma[0, n] - 2)*DivisorSigma[0, m]/2]+1; t[1, 1] = 1; t[1, _] = 0; ft = Flatten[ Table[ t[n-m+1, m], {n, 1, rows}, {m, n, 1, -1}]] (* From Jean-François Alcover, Nov 18 2011, after Franklin T. Adams-Watters *)
|
|
|
CROSSREFS
| Cf. A108461. Column 1: A001055. Main diagonal: A051707.
Sequence in context: A088432 A071466 A155041 * A193759 A117468 A116374
Adjacent sequences: A108452 A108453 A108454 * A108456 A108457 A108458
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Jun 03 2005
|
| |
|
|
