A302142 a(n) = (-1) * round(j((1 + sqrt(-n))/2)), where j is j-invariant.

-1728, -233, 0, 90, 539, 1539, 3375, 6511, 11663, 19897, 32768, 52512, 82306, 126616, 191658, 286008, 421407, 613808, 884736, 1263051, 1787217, 2508208, 3493226, 4830420, 6634880, 9056199, 12288000, 16579887, 22252407, 29715715, 39492794, 52248279, 68824132

Offset: 1

Author

Seiichi Manyama, Jun 04 2018

Keywords

• sign

Comments

a(n) is close to A056580(n) - 744.

Examples

			   n | j((1 + sqrt(-n))/2) |   a(n)  | A056580(n) - 744
  ---+---------------------+---------+------------------
   1 |       -1728         |   -1728 |             -721
   2 |        -232.86...   |    -233 |             -659
   3 |           0         |       0 |             -513
   4 |          89.59...   |      90 |             -209
   5 |         538.90...   |     539 |              380
   6 |        1539.19...   |    1539 |             1454
   7 |        3375         |    3375 |             3328
   8 |        6511.17...   |    6511 |             6484
   9 |       11663.39...   |   11663 |            11648
  10 |       19897.28...   |   19897 |            19888
  11 |       32768         |   32768 |            32762
  12 |       52511.98...   |   52512 |            52508
  13 |       82306.31...   |   82306 |            82304
  14 |      126616.31...   |  126616 |           126615
  15 |      191657.83...   |  191658 |           191657
  16 |      286007.99...   |  286008 |           286007
  17 |      421407.46...   |  421407 |           421407
  18 |      613808.31...   |  613808 |           613808
  19 |      884736         |  884736 |           884736
  20 |     1263050.90...   | 1263051 |          1263051
  21 |     1787216.60...   | 1787217 |          1787216
  22 |     2508208.07...   | 2508208 |          2508208
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, j-Function

Crossrefs

Cf. A000521, A056580, A305500.

Programs

PARI

{a(n) = -round(ellj((1+sqrt(n)*I)/2))}