A014600 -id:A014600 - cp's OEIS frontend

A305474 Coefficients of Hilbert class polynomial H_D(x) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

0, 1, -1728, 1, 3375, 1, -8000, 1, 32768, 1, -54000, 1, -121287375, 191025, 1, -287496, 1, 884736, 1, -681472000, -1264000, 1, 12771880859375, -5151296875, 3491750, 1, 14670139392, -4834944, 1, 12288000, 1, -16581375, 1, 1566028350940383, -58682638134

Offset: 1

Seiichi Manyama, Jun 02 2018

			D   |                0             1         2  3
----+---------------------------------------------
-3  |                0,            1;
-4  |            -1728,            1;
-7  |             3375,            1;
-8  |            -8000,            1;
-11 |            32768,            1;
-12 |           -54000,            1;
-15 |       -121287375,       191025,        1;
-16 |          -287496,            1;
-19 |           884736,            1;
-20 |       -681472000,     -1264000,        1;
-23 |   12771880859375,  -5151296875,  3491750, 1;
-24 |      14670139392,     -4834944,        1;
-27 |         12288000,            1;
-28 |        -16581375,            1;
-31 | 1566028350940383, -58682638134, 39491307, 1;
-32 |      12167000000,    -52250000,        1;
-35 |    -134217728000,    117964800,        1;
-36 |   -1790957481984,   -153542016,        1;

Seiichi Manyama, Rows n = 1..250, flattened

Cf. A014600, A014601, A032354, A305475 (constant).

d(n) = 2*n+n%2;
T(n, k) = polcoef(polclass(-d(n)), k);
tabf(nn) = for(n=1, nn, for(k=0, poldegree(polclass(-d(n))), print1(T(n, k), ", ")); print)

A225060 Discriminants D < 0 such that h(D) > h(D') for D < D' < 0, negated.

Original entry on oeis.org

3, 15, 23, 39, 47, 71, 95, 119, 167, 191, 215, 239, 311, 431, 479, 551, 671, 719, 791, 839, 959, 1151, 1319, 1511, 1559, 1679, 1991, 2159, 2351, 2519, 2831, 2999, 3071, 3671, 3839, 3911, 4031, 4079, 4199, 4679, 4991, 5351, 5519, 5591, 5711, 6431, 6551, 7391, 8111

Offset: 1

Charles R Greathouse IV, Apr 26 2013

nonn

Essentially records in A014600.

H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford 5 (1934), pp. 293-301.

Charles R Greathouse IV, Table of n, a(n) for n = 1..675

Cf. A014600, A225061, A038552.

r=0;forstep(n=3,1e6,[1,3],t=qfbclassno(-n);if(t>r,r=t;print1(n", ")))

A225061 Record class numbers of discriminants of imaginary quadratic fields: h(-A225060(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 15, 19, 21, 25, 26, 30, 31, 32, 33, 36, 41, 45, 49, 51, 52, 56, 60, 63, 64, 68, 73, 76, 81, 82, 83, 84, 85, 88, 91, 92, 93, 97, 99, 109, 114, 117, 120, 121, 126, 134, 135, 138, 139, 153, 156, 161, 165, 174, 178, 181, 185, 195, 202, 205

Offset: 1

Charles R Greathouse IV, Apr 26 2013

nonn

H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford 5 (1934), pp. 293-301.

Charles R Greathouse IV, Table of n, a(n) for n = 1..675

Cf. A014600, A225060, A038552.

r=0;forstep(n=3,1e6,[1,3],t=qfbclassno(-n);if(t>r,print1(r=t", ")))

cp's OEIS Frontend

A305474 Coefficients of Hilbert class polynomial H_D(x) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

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A225060 Discriminants D < 0 such that h(D) > h(D') for D < D' < 0, negated.

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PARI

A225061 Record class numbers of discriminants of imaginary quadratic fields: h(-A225060(n)).

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Author

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PARI