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%I #83 Feb 16 2025 08:33:53
%S -1728,-233,0,90,539,1539,3375,6511,11663,19897,32768,52512,82306,
%T 126616,191658,286008,421407,613808,884736,1263051,1787217,2508208,
%U 3493226,4830420,6634880,9056199,12288000,16579887,22252407,29715715,39492794,52248279,68824132
%N a(n) = (-1) * round(j((1 + sqrt(-n))/2)), where j is j-invariant.
%C a(n) is close to A056580(n) - 744.
%H Seiichi Manyama, <a href="/A302142/b302142.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/j-Function.html">j-Function</a>
%e n | j((1 + sqrt(-n))/2) | a(n) | A056580(n) - 744
%e ---+---------------------+---------+------------------
%e 1 | -1728 | -1728 | -721
%e 2 | -232.86... | -233 | -659
%e 3 | 0 | 0 | -513
%e 4 | 89.59... | 90 | -209
%e 5 | 538.90... | 539 | 380
%e 6 | 1539.19... | 1539 | 1454
%e 7 | 3375 | 3375 | 3328
%e 8 | 6511.17... | 6511 | 6484
%e 9 | 11663.39... | 11663 | 11648
%e 10 | 19897.28... | 19897 | 19888
%e 11 | 32768 | 32768 | 32762
%e 12 | 52511.98... | 52512 | 52508
%e 13 | 82306.31... | 82306 | 82304
%e 14 | 126616.31... | 126616 | 126615
%e 15 | 191657.83... | 191658 | 191657
%e 16 | 286007.99... | 286008 | 286007
%e 17 | 421407.46... | 421407 | 421407
%e 18 | 613808.31... | 613808 | 613808
%e 19 | 884736 | 884736 | 884736
%e 20 | 1263050.90... | 1263051 | 1263051
%e 21 | 1787216.60... | 1787217 | 1787216
%e 22 | 2508208.07... | 2508208 | 2508208
%o (PARI) {a(n) = -round(ellj((1+sqrt(n)*I)/2))}
%Y Cf. A000521, A056580, A305500.
%K sign,changed
%O 1,1
%A _Seiichi Manyama_, Jun 04 2018