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%I #6 Jun 24 2014 01:08:32
%S 0,0,0,1,1,1,2,2,2,3,3,5,4,4,5,6,4,8,6,8,6,8,8,11,7,10,10,12,10,12,10,
%T 13,10,15,12,15,10,17,16,17,13,18,16,18,16,19,18,21,13,20,19,25,20,23,
%U 19,24,20,25,24,27,19,24,26,28,21,28,25,30,26,31,26,32,19,30,30,33,30
%N Number of partitions into two parts which have different prime signatures.
%C The 'prime signature' of n is the sorted list of exponents in the prime factorization of n.
%C Does lim n->infinity a(n)/n exist? If not, what are the limsup and liminf of a(n)/n?
%e a(9) = 3; the partitions are 8+1, 6+3 and 5+4.
%t sig[n_] := Sort[Last/@FactorInteger[n]]; a[n_] := Length[Select[Range[Floor[n/2]], sig[ # ]!=sig[n-# ]&]]
%Y Cf. A077564.
%K nonn
%O 0,7
%A _Amarnath Murthy_, Nov 11 2002
%E Edited by _Dean Hickerson_, Nov 11 2002
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