OFFSET
1,2
COMMENTS
Positive values of triangle A168021.
Note that column 1 lists the numbers of partitions A000041(n).
Row n has A000005(n) terms.
Also, it appears that row n lists the partition numbers of the divisors of n, in decreasing order. [Omar E. Pol, Nov 23 2009]
LINKS
EXAMPLE
For example:
Consider row 8: (22, 5, 2, 1). The divisors of 8 are 1, 2, 4, 8 (see A027750). Also, there are 22 partitions of 8 into parts divisible by 1 (A000041(8)=22); 5 partitions of 8 into parts divisible by 2: {(8),(6+2),(4+4),(4+2+2),(2+2+2+2)}; 2 partitions of 8 into parts divisible by 4: {(8),(4+4)}; and 1 partition of 8 into parts divisible by 8. Then row 8 is formed by 22, 5, 2, 1.
Triangle begins:
1;
2, 1;
3, 1;
5, 2, 1;
7, 1;
11, 3, 2, 1;
15, 1;
22, 5, 2, 1;
30, 3, 1;
42, 7, 2, 1;
56, 1;
77, 11, 5, 3, 2, 1;
MAPLE
A168018 := proc(n) local dvs, p, i, d, a, pp, divs, par; dvs := sort(convert(numtheory[divisors](n), list)) ; p := combinat[partition](n) ; for i from 1 to nops(dvs) do d := op(i, dvs) ; a := 0 ; for pp in p do divs := true; for par in pp do if par mod d <> 0 then divs := false; end if; end do ; if divs then a := a+1 ; end if; end do ; printf("%d, ", a) ; end do ; end proc: for n from 1 to 40 do A168018(n) ; end do : # R. J. Mathar, Feb 05 2010
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Nov 22 2009
EXTENSIONS
Terms beyond row 12 from R. J. Mathar, Feb 05 2010
STATUS
approved