A239508 - OEIS

%I #3 Mar 21 2014 08:59:53

%S 1,1,1,1,1,1,2,2,2,2,3,3,4,4,5,6,7,7,8,8,10,12,14,14,16,17,20,22,25,

%T 26,31,33,37,40,45,49,57,60,66,71,80,86,98,104,115,125,138,147,164,

%U 175,193,209,230,244,269,289,318,343,374,398,437,468,510,548

%N Number of partitions of n into nonprime squarefree numbers, cf. A000469.

%e a(10) = #{10, 6+1+1+1+1, 10x1} = 3;

%e a(11) = #{10+1, 6+1+1+1+1+1, 11x1} = 3;

%e a(12) = #{10+1+1, 6+6, 6+6x1, 12x1} = 4;

%e a(13) = #{10+1+1+1, 6+6+1, 6+7x1, 13x1} = 4;

%e a(14) = #{14, 10+1+1+1+1, 6+6+1+1, 6+8x1, 14x1} = 5;

%e a(15) = #{15, 14+1, 10+5x1, 6+6+1+1+1, 6+9x1, 15x1} = 6;

%e a(16) = #{15+1, 14+1+1, 10+6, 10+6x1, 6+6+4x1, 6+10x1, 16x1} = 7.

%o (Haskell)

%o a239508 = p a000469_list where

%o    p _          0 = 1

%o    p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m

%Y Cf. A239509, A073576.

%K nonn

%O 0,7

%A _Reinhard Zumkeller_, Mar 21 2014