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Refines sequence A078812 using permutations and products of exponents on least prime signatures.
3

%I #3 Mar 31 2012 13:23:37

%S 1,2,1,3,4,1,4,6,4,6,1,5,8,12,9,12,8,1,6,10,16,9,12,36,8,12,24,10,1,7,

%T 12,20,24,15,48,36,27,16,72,32,15,40,12,1,8,14,24,30,16,18,60,48,72,

%U 54,20,96,144,54,16,20,120,80,18,60,14,1

%N Refines sequence A078812 using permutations and products of exponents on least prime signatures.

%C The shape sequence for this table is A000041. Row sums in the example are A000079, A006906 and A001906.

%e When the signatures (A025487) are listed in A036035 order the number of permutations of the exponents begin

%e 1, 1 1, 1 2 1, 1 2 1 3 1, 1 2 2 3 3 4 1, ... b(n) and the products begin

%e 1, 2 1, 3 2 1, 4 3 4 2 1, 5 4 6 3 4 2 1, ... c(n) thus we can write

%e 1, 2 1, 3 4 1, 4 6 4 6 1, 5 8 12 9 12 8 1, ... a(n) = b(n)*c(n)

%Y Cf. A078812.

%K nonn,tabf

%O 1,2

%A _Alford Arnold_, Aug 15 2003