Unique solutions (requiring an odd power) to Pillai's equation for n <= 1000

Perfect powers examined up to 2^63-1

n for which there is a unique solution requiring an odd power:

  1,   2,  10,  30,  38,  46, 122, 126, 138, 142, 146, 150, 154, 166, 170, 190, 
194, 214, 222, 234, 270, 282, 298, 318, 338, 342, 354, 370, 382, 386, 406, 486, 
490, 498, 502, 518, 546, 550, 566, 574, 582, 586, 594, 638, 666, 678, 686, 694, 
710, 726, 730, 734, 746, 774, 806, 814, 818, 834, 838, 878, 894, 906, 930, 934, 
938, 962, 970, 974, 982

Total number of solutions: 69

Solutions for each n:

  1 = 3^2 - 2^3

  2 = 3^3 - 5^2

 10 = 13^3 - 3^7

 30 = 83^2 - 19^3

 38 = 37^2 - 11^3

 46 = 17^2 - 3^5

122 = 3^5 - 11^2

126 = 15^3 - 57^2

138 = 173^2 - 31^3

142 = 13^2 - 3^3

146 = 195^3 - 2723^2

150 = 175^3 - 2315^2

154 = 111^2 - 23^3

166 = 7^5 - 129^2

170 = 59^3 - 453^2

190 = 39^2 - 11^3

194 = 3^5 - 7^2

214 = 49^2 - 3^7

222 = 7^3 - 11^2

234 = 3^5 - 3^2

270 = 39^3 - 9^5

282 = 25^2 - 7^3

298 = 19^3 - 81^2

318 = 7^3 - 5^2

338 = 3^7 - 43^2

342 = 7^3 - 1^2

354 = 131^2 - 7^5

370 = 11^3 - 31^2

382 = 25^2 - 3^5

386 = 9^3 - 7^3

406 = 1107^2 - 107^3

486 = 9^3 - 3^5

490 = 11^3 - 29^2

498 = 29^2 - 7^3

502 = 23^2 - 3^3

518 = 43^2 - 11^3

546 = 43^3 - 281^2

550 = 31^3 - 171^2

566 = 15^3 - 53^2

574 = 365^2 - 51^3

582 = 283^2 - 43^3

586 = 115^3 - 1233^2

594 = 63^2 - 15^3

638 = 549^2 - 67^3

666 = 3^7 - 39^2

678 = 7^5 - 127^2

686 = 2395^2 - 179^3

694 = 45^2 - 11^3

710 = 87^2 - 19^3

726 = 55^3 - 407^2

730 = 3511^2 - 231^3

734 = 15^5 - 871^2

746 = 33^2 - 7^3

774 = 15^3 - 51^2

806 = 209^2 - 35^3

814 = 29^2 - 3^3

818 = 3^7 - 37^2

834 = 175^2 - 31^3

838 = 55^2 - 3^7

878 = 47^2 - 11^3

894 = 7^7 - 907^2

906 = 409^2 - 55^3

930 = 19^3 - 77^2

934 = 31^2 - 3^3

938 = 5^5 - 3^7

962 = 3^7 - 35^2

970 = 11^3 - 19^2

974 = 15^3 - 49^2

982 = 35^2 - 3^5