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EXAMPLE
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The integer partitions of 4 are {(4), (3,1), (2,2), (2,1,1), (1,1,1,1)}, with multiset union {1,1,1,1,1,1,1,2,2,2,3,4}, with multiplicities (7,3,1,1), so a(4) = prime(7)*prime(3)*prime(1)*prime(1) = 340.
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
6: {1,2}
28: {1,1,4}
340: {1,1,3,7}
3108: {1,1,2,4,12}
106932: {1,1,2,4,8,19}
2732340: {1,1,2,3,6,11,30}
236790060: {1,1,2,3,6,9,19,45}
19703562780: {1,1,2,3,5,8,15,26,67}
3419598096420: {1,1,2,3,5,8,13,21,41,97}
674127752953380: {1,1,2,3,5,7,12,18,31,56,139}
264134168649181380: {1,1,2,3,5,7,12,17,28,45,83,195}
95825592671995399620: {1,1,2,3,5,7,11,16,25,38,63,112,272}
67662122741507082338220: {1,1,2,3,5,7,11,16,24,35,55,87,160,373}
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