a(n,m) tabf head (staircase) for A064364 (note the changed offset and the extra 0) Product of parts of partitions of n with only prime parts. For n=0 one takes 1 in order to have row sums A002098(n) for n>=0. For n=1 one takes 0 (not 1 like in A064364 in order to a have a paermutation of the positive integers) because 1 is not a member of A001414. So, actually one should take offset 0 and include 0. Then one has a permutation of the nonnegative numbers. This changes sequence A064364 would be [1,0,2,3,4,5,6,8,9,...] n\m 1 2 3 4 5 6 7 8 9 10 11 12 ... 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 5 5 6 0 0 0 0 0 0 0 0 0 0 6 8 9 0 0 0 0 0 0 0 0 0 0 7 7 10 12 0 0 0 0 0 0 0 0 0 8 15 16 18 0 0 0 0 0 0 0 0 0 9 14 20 24 27 0 0 0 0 0 0 0 0 10 21 25 30 32 36 0 0 0 0 0 0 0 11 11 28 40 45 48 54 0 0 0 0 0 0 12 35 42 50 60 64 72 81 0 0 0 0 0 13 13 22 56 63 75 80 90 96 108 0 0 0 14 33 49 70 84 100 120 128 135 144 162 0 0 15 26 44 105 112 125 126 150 160 180 192 216 243 . . . n\m 1 2 3 4 5 6 7 8 9 10 11 12 ... For the partitons with only prime parts which have these products see arrays A116864 and A116865. Column m=1 sequence is A056240(n),n>=2. The last nonvanishing numbers in each row give A000792(n), n>=2. ################################################# e.o.f.#####################################################