OFFSET
0,3
COMMENTS
Note that for positive integers the number of partitions of n such that all parts are equal is equal to the number of proper divisors of n. (A032741(n)).
LINKS
EXAMPLE
The partitions of 6 are:
6 .............. All parts are distinct ..... (1).
5+1 ............ All parts are distinct ..... (2).
4+2 ............ All parts are distinct ..... (3).
4+1+1 .......... Only some parts are equal.
3+3 ............ All parts are equal ........ (4).
3+2+1 .......... All parts are distinct ..... (5).
3+1+1+1 ........ Only some parts are equal.
2+2+2 .......... All parts are equal ........ (6).
2+2+1+1 ........ Only some parts are equal.
2+1+1+1+1 ...... Only some parts are equal.
1+1+1+1+1+1 .... All parts are equal ........ (7).
So a(6) = 7.
MATHEMATICA
ds[n_]:=Module[{lun=Length[Union[n]]}, Length[n]==lun||lun==1]; Table[ Count[ IntegerPartitions[n], _?(ds)], {n, 0, 60}] (* Harvey P. Dale, Sep 13 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 15 2009
EXTENSIONS
More terms from D. S. McNeil, May 10 2010
STATUS
approved