A374229
a(n) is the smallest number which can be represented as the sum of three distinct n-th powers of primes in exactly n ways, or -1 if no such number exists.
Original entry on oeis.org
10, 414, 8627527
Offset: 1
a(2) = 414 = 2^2 + 7^2 + 19^2 = 2^2 + 11^2 + 17^2.
A374230
a(n) is the smallest number which can be represented as the sum of four distinct n-th powers of primes in exactly n ways, or -1 if no such number exists.
Original entry on oeis.org
17, 423, 435888, 199898912404
Offset: 1
a(2) = 423 = 2^2 + 3^2 + 7^2 + 19^2 = 2^2 + 3^2 + 11^2 + 17^2.
A374270
a(n) is the smallest number which can be represented as the sum of n distinct n-th powers of primes in exactly 2 ways, or -1 if no such number exists.
Original entry on oeis.org
-1, 410, 185527, 6539044, 2250298051, 1397942436813, 56190747296833091
Offset: 1
a(2) = 410 = 7^2 + 19^2 = 11^2 + 17^2.
a(3) = 185527 = 13^3 + 43^3 + 47^3 = 19^3 + 31^3 + 53^3.
A374271
a(n) is the smallest number which can be represented as the sum of n distinct n-th powers of primes in exactly 3 ways, or -1 if no such number exists.
Original entry on oeis.org
-1, 2210, 8627527, 616151524, 876639080351
Offset: 1
a(2) = 2210 = 19^2 + 43^2 = 23^2 + 41^2 = 29^2 + 37^2.
a(3) = 8627527 = 19^3 + 151^3 + 173^3 = 23^3 + 139^3 + 181^3 = 71^3 + 73^3 + 199^3.
A374272
a(n) is the smallest number which can be represented as the sum of n distinct n-th powers of primes in exactly 4 ways, or -1 if no such number exists.
Original entry on oeis.org
-1, 10370, 999979163, 199898912404
Offset: 1
a(2) = 10370 = 13^2 + 101^2 = 31^2 + 97^2 = 59^2 + 83^2 = 71^2 + 73^2.
a(3) = 999979163 = 83^3 + 757^3 + 827^3 = 107^3 + 677^3 + 883^3 = 197^3 + 523^3 + 947^3 = 281^3 + 419^3 + 967^3.
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