OFFSET
0,4
COMMENTS
The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.
EXAMPLE
a(7) = 4. The partitions are 7, 6+1, 4+3, 4+2+1. (5+2, 3+2+2, ... are not counted.)
MATHEMATICA
sig[n_] := Sort[Last/@FactorInteger[n]]; f[n_, m_] := Module[{sm}, If[n>m(m+1)/2||n<0, Return[{}]]; If[n==0, Return[{{}}]]; sm=sig[m]; f[n, m]=Union[f[n, m-1], Prepend[ #, m]&/@Select[f[n-m, m-1], !MemberQ[sig/@#, sm]&]]]; a[n_] := Length[f[n, n]] (* f[n, m] is list of partitions of n into parts <= m with distinct prime signatures *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 11 2002
EXTENSIONS
Edited by Dean Hickerson, Nov 11 2002
STATUS
approved