sum of more than one A137701

[Jonathan Post]

A137701  Semiprime(n)^prime(n).
A111096  Sum of semiprime(n)^prime(n)

The two above should crossreference each other.

new: sum of more than one distinct A137701 (comment: A111096 is a subset).

I'm especially interested in the subset of primes in the new sequence.

Would anyone like to extend the below, especially to search for primes?

{n}   sum
1,2    4^2 + 6^3 = 232
1,3    16 + 59049 = 59065
2,3    216 + 59049 = 59265
1,2,3  4^2 + 6^3 + 9^5 = 59281 which is prime
1,4    16 + 10000000 = 10000016
2,4    216 + 10000000 = 10000216
1,2,4  16 + 216 + 10000000 = 10000232
3,4    59049 + 10000000 = 10059049
1,3,4  16 + 59049 + 10000000 = 10059065
2,3,4  6^3 + 9^5 + 10^7 = 10059265
1,2,3,4   10059281 = 4^2 + 6^3 + 9^5 + 10^7, which is prime
1,5    16 + 4049565169664 = 4049565169680
2,5    216 + 4049565169664 = 4049565169880
3,5    59049 + 4049565169664 = 4049565228713 which is prime
1,2,5  16 + 216 + 4049565169664 = 4049565169896
1,3,5  16 + 59049 + 4049565169664 = 4049565228729
2,3,5  216 + 59049 + 4049565169664 = 4049565228929
1,2,3,5  16 + 216 + 59049 + 4049565169664 = 4049565228945
1,6    16 + 1946195068359375 = 1946195068359391 which is prime
2,6    216 + 1946195068359375 = 1946195068359591
1,2,6   16 + 216 + 1946195068359375 = 1946195068359607
3,6     59049 + 1946195068359375 = 1946195068418424
1,3,6  16 + 59049 + 1946195068359375 = 1946195068418440
2,3,6  216 + 59049 + 1946195068359375 = 1946195068418640
1,2,3,6  16 + 216 + 59049 + 1946195068359375 = 1946195068418656
4,5     10000000 + 4049565169664 = 4049575169664
1,4,5  16 + 10000000 + 4049565169664 = 4049575169680
2,4,5  216 + 10000000 + 4049565169664 = 4049575169880
1,2,4,5  16 + 216 + 10000000 + 4049565169664 = 4049575169896
3,4,5  59049 + 10000000 + 4049565169664 = 4049575228713
1,3,4,5  16 + 59049 + 10000000 + 4049565169664 = 4049575228729
2,3,4,5  216 + 59049 + 10000000 + 4049565169664 = 4049575228929
1,2,3,4,5  16 + 216 + 59049 + 10000000 + 4049565169664 = 4049575228945
4,6     10000000 + 1946195068359375 = 1946195078359375
1,4,6  16 + 10000000 + 1946195068359375 = 1946195078359391
2,4,6  216 + 10000000 + 1946195068359375
1,2,4,6  16 + 216 + 10000000 + 1946195068359375 = 1946195078359607
3,4,6  59049 + 10000000 + 1946195068359375 = 1946195078418424
1,3,4,6  16 + 59049 + 10000000 + 1946195068359375 = 1946195078418440
2,3,4,6  216 + 59049 + 10000000 + 1946195068359375 = 1946195078418640
1,2,3,4,6  16 + 216 + 59049 + 10000000 + 1946195068359375 = 1946195078418656
5,6     4049565169664 + 1946195068359375 = 1950244633529039
1,5,6  16 + 4049565169664 + 1946195068359375 = 1950244633529055
2,5,6  216 + 4049565169664 + 1946195068359375 = 1950244633529255
1,2,5,6  16 + 216 + 4049565169664 + 1946195068359375 = 1950244633529271
3,5,6  59049 + 4049565169664 + 1946195068359375 = 1950244633588088
4,5,6  10000000 + 4049565169664 + 1946195068359375
1,4,5,6 16 + 10000000 + 4049565169664 + 1946195068359375 = 1950244643529055
2,4,5,6  216 + 10000000 + 4049565169664 + 1946195068359375 = 1950244643529255
3,4,5,6  59049 + 10000000 + 4049565169664 + 1946195068359375 = 1950244643588088
1,3,4,5,6  16 + 59049 + 10000000 + 4049565169664 + 1946195068359375 =
1950244643588104
2,3,4,5,6  216 + 59049 + 10000000 + 4049565169664 + 1946195068359375 =
1950244643588304
1,2,3,4,5,6  16 + 216 + 59049 + 10000000 + 4049565169664 +
1946195068359375 = 1950244643588320
1,7    16 + 30041942495081691894741 = 30041942495081691894757
1,2,7  16 + 216 + 30041942495081691894741 = 30041942495081691894973

etc.