Position of S000537(n) in the list of powers A001597.
3, 6, 1, 15, 2, 8, 14, 7, 4, 216, 361, 5, 20, 295, 60, 72, 75, 61, 9, 22, 88, 10, 1257, 16, 11, 31, 328, 431, 384026, 21, 26, 12, 25, 23268, 19, 13, 57, 41, 745174, 17, 245, 2738, 18, 30, 264, 416, 103, 109, 23, 24, 46, 53, 4048, 47, 27, 40, 128, 67, 28, 29, 120, 32, 52, 570, 179, 33, 595, 34, 35, 188
1
Powers up to 10^17 were computed to create this sequence.
T. D. Noe, Plot of 70 terms
(Mma) nn = 10^12; mx = Floor[Log[2, nn]]; s = Union[Flatten[Table[Table[i^k, {i, nn^(1/k)}], {k, 2, mx}]]]; d = Differences[s]; Flatten[Table[Position[d, n], {n, 53}]]
Cf. A001597, A189117, S000537.
nonn,hard
T. D. Noe, Mar 12 2015