%I #8 Jun 24 2014 01:08:33

%S 1,1,1,2,2,2,3,4,4,5,6,8,10,10,11,14,14,19,22,22,25,30,34,38,40,46,54,

%T 60,63,74,81,85,91,108,118,126,134,153,173,180,186,214,236,245,262,

%U 301,326,338,355,395,437,461,476,540,592,610,649,717,768,811,853,943,1039

%N Number of partitions of n into parts with distinct prime signatures.

%C The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.

%e a(7) = 4. The partitions are 7, 6+1, 4+3, 4+2+1. (5+2, 3+2+2, ... are not counted.)

%t 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 *)

%Y Cf. A077563.

%K nonn

%O 0,4

%A _Amarnath Murthy_, Nov 11 2002

%E Edited by _Dean Hickerson_, Nov 11 2002