a(n,k)  tabf head (staircase) for  A116865
  
  Characteristic array for partitions of n with only prime parts, using Abramowitz-Stegun (A-St) ordering of partitions of n.
  The entry in row n is 1 iff the partition of n in A-St order has only prime parts.
  
  
  n\k   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
 
  1     0  

  2     1  0

  3     1  0  0  

  4     0  0  1  0  0  

  5     1  0  1  0  0  0  0

  6     0  0  0  1  0  0  1  0  0  0  0 

  7     1  0  1  0  0  0  0  1  0  0  0  0  0  0  0 
 
  8     0  0  0  1  0  0  0  0  0  1  0  0  0  0  1  0  0  0  0  0  0  0  
 
  9     0  0  1  0  0  0  0  0  0  1  0  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0 

 10     0  0  0  1  0  1  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0

   .
   .
   .

  n\k   1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42



 The sequence of row lengths is A000041: [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...] (partition numbers).

 One could add the row for n=0 with a 0, if the part 0 is considered for n=0, and only for this n.
 
 For n=0 a 1 should be used in order to have the row sums A000607(n), n>=0. 

 E.g. a(4,3) refers to the third partition of n=4 in the A-St order, namely (2,2), which has only prime parts, whence a(4,3)=1.
 
 E.g. a(4,4) refers to the fourth partition of n=4 in this ordering, namely (1^2,2)=(2,1,1), whence a(4,4)=0 because 1 is not prime. 
    
 The row sums give the number of partitions of n with only prime parts, A000607(n)= [0,1,1,1,2,2,3,3,4,5,,,,]. n>=1.

 Compare with the array A116864 which gives the product of parts of these partitions with only prime parts.

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