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EXAMPLE
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The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)}, with multiset union {1,1,2,2,3,4,5,6}, with multiplicities (2,2,1,1,1,1), so a(6) = prime(1)^4*prime(2)^2 = 144.
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
2: {1}
8: {1,1,1}
8: {1,1,1}
32: {1,1,1,1,1}
144: {1,1,1,1,2,2}
432: {1,1,1,1,2,2,2}
2160: {1,1,1,1,2,2,2,3}
27000: {1,1,1,2,2,2,3,3,3}
582120: {1,1,1,2,2,2,3,4,4,5}
7623000: {1,1,1,2,2,3,3,3,4,5,5}
336936600: {1,1,1,2,2,3,3,4,5,5,6,7}
6740402760: {1,1,1,2,2,3,4,4,4,6,6,7,8}
543454231320: {1,1,1,2,2,3,4,4,5,6,7,8,9,10}
57619849046760: {1,1,1,2,2,3,4,5,5,6,8,9,10,11,12}
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