A003273 -id:A003273 - cp's OEIS frontend

A248401 Noncongruent squarefree numbers n with A248394(n)/d(n) = 3, where d(n) = A000005(n).

43, 131, 163, 417, 491, 537, 571, 619, 849, 913, 923, 1019, 1187, 1203, 1579, 1641, 1707, 1747, 1779, 1835, 1843, 1907, 2003, 2051, 2123, 2203, 2227, 2235, 2315, 2537, 2563, 2649, 2747, 2787, 2913, 2931, 3083, 3107, 3307, 3345, 3363, 3561, 3587, 3611, 3651, 3659

Offset: 1

N. J. A. Sloane, Oct 20 2014

nonn

J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Cf. A000005, A003273, A165564, A248394, A248395, A248397-A248407.

More terms from Amiram Eldar, Oct 13 2019

A248402 Noncongruent squarefree numbers n with A248394(n)/d(n) = -3, where d(n) = A000005(n).

Original entry on oeis.org

107, 251, 283, 331, 547, 633, 643, 699, 737, 771, 883, 1041, 1147, 1163, 1307, 1459, 1483, 1497, 1523, 1531, 1619, 1627, 1699, 1793, 1883, 1915, 1923, 2049, 2179, 2251, 2283, 2361, 2363, 2411, 2427, 2433, 2443, 2467, 2539, 2651, 2843, 2971, 3091, 3147, 3187, 3203

Offset: 1

N. J. A. Sloane, Oct 20 2014

nonn

J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Cf. A000005, A003273, A248394, A248395, A248397-A248406.

More terms from Amiram Eldar, Oct 13 2019

A248403 Noncongruent squarefree numbers n with A248395(n)/d(n) = 1, where d(n) = A000005(n).

Original entry on oeis.org

2, 10, 58, 74, 114, 122, 130, 170, 258, 290, 314, 346, 354, 362, 370, 402, 474, 506, 586, 610, 618, 642, 714, 730, 746, 786, 826, 906, 922, 946, 962, 970, 986, 1066, 1074, 1090, 1162, 1194, 1218, 1258, 1306, 1338, 1378, 1474, 1506, 1514, 1554, 1562, 1626, 1658

Offset: 1

N. J. A. Sloane, Oct 20 2014

nonn

J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Cf. A000005, A003273, A248394, A248395, A248397-A248406.

More terms from Amiram Eldar, Oct 13 2019

A248404 Noncongruent squarefree numbers n with A248395(n)/d(n) = -1, where d(n) = A000005(n).

Original entry on oeis.org

26, 42, 66, 106, 186, 202, 266, 418, 498, 530, 554, 570, 634, 682, 690, 754, 762, 770, 834, 858, 874, 930, 1010, 1034, 1082, 1114, 1130, 1266, 1290, 1298, 1354, 1370, 1410, 1490, 1570, 1586, 1634, 1698, 1834, 1930, 1946, 1986, 1994, 2002, 2074, 2082, 2090, 2146

Offset: 1

N. J. A. Sloane, Oct 20 2014

nonn

J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Cf. A000005, A003273, A248394, A248395, A248397-A248406.

More terms from Amiram Eldar, Oct 13 2019

A248405 Noncongruent squarefree numbers n with A248395(n)/d(n) = 2, where d(n) = A000005(n).

Original entry on oeis.org

82, 282, 562, 626, 818, 914, 1042, 1106, 1138, 1202, 1426, 1442, 1578, 1618, 1778, 1802, 1874, 2114, 2258, 2338, 2410, 2482, 2506, 2562, 2642, 2674, 2714, 2866, 2874, 2938, 2954, 3322, 3498, 3506, 3602, 3810, 4314, 4354, 4458, 4562, 4826, 4930, 5026, 5258, 5322

Offset: 1

N. J. A. Sloane, Oct 20 2014

nonn

J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334.

Cf. A000005, A003273, A248394, A248395, A248397-A248406.

More terms from Amiram Eldar, Oct 13 2019

A259681 Let m = A062695(n); a(n) is value of t in decomposition of m defined in Comments.

Original entry on oeis.org

2, 1, 1, 1, 1, 5, 2, 7, 2, 2, 3, 2, 1, 1, 3, 13, 1, 19, 5, 1, 7, 2, 1, 10, 1, 31, 26, 1, 15, 5, 2, 6, 1, 2, 1, 3, 47, 2, 1, 1, 3, 43, 1, 3, 1, 2, 7, 10, 5, 15, 1, 1, 1, 59, 1, 1, 1, 1, 1, 2, 13, 1, 191, 2, 1, 1, 31, 15, 2, 5, 1, 1, 1, 1, 2, 1, 5, 13, 2, 7, 19

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Cf. A003273, A006991, A062695, A259680-A259687.

More terms from Jinyuan Wang, Jan 01 2021

A259682 Let m = A062695(n); a(n) is value of u in decomposition of m defined in Comments.

Original entry on oeis.org

1, 1, 5, 1, 23, 1, 7, 1, 1, 3, 1, 1, 257, 5, 1, 23, 1, 1, 1, 1, 1, 1, 79, 1, 71, 1, 17, 457, 1, 1, 1, 1, 1, 7, 21, 1, 1, 1, 1, 103, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 5, 47, 199, 1, 7, 37, 1081, 13, 3, 17, 3, 1, 3, 1, 7, 167, 19, 1, 1, 239, 1, 1, 1, 1, 1, 1, 1, 103

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Cf. A003273, A006991, A062695, A259680-A259687.

More terms from Jinyuan Wang, Jan 01 2021

A259683 Let m = A062695(n); a(n) is value of v in decomposition of m defined in Comments.

Original entry on oeis.org

17, 41, 13, 1, 1, 1, 11, 23, 1, 7, 1, 113, 1, 53, 97, 1, 313, 1, 11, 353, 1, 193, 1, 1, 1, 7, 1, 1, 31, 1, 1, 13, 33, 43, 29, 31, 7, 1, 1, 1, 241, 1, 1, 7, 1, 433, 127, 89, 1, 1, 197, 1, 1, 17, 1, 29, 1, 85, 53, 33, 29, 1, 1, 577, 15, 1, 1, 79, 1, 1, 1201, 1, 1241

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Cf. A003273, A006991, A062695, A259680-A259687.

More terms from Jinyuan Wang, Jan 01 2021

A259684 Let m = A062695(n); a(n) is value of a in decomposition of m defined in Comments.

Original entry on oeis.org

3, 5, 3, 5, 2, 1, 3, 4, 1, 1, 1, 9, 153, 7, 7, 6, 13, 5, 1, 17, 1, 11, 4, 1, 4, 4, 11, 253, 4, 1, 1, 1, 1, 5, 5, 2, 8, 1, 1, 4, 103, 39, 29, 2, 5, 19, 8, 7, 1, 1, 163, 4, 8, 63, 44, 23, 35, 7, 2, 5, 4, 5, 13, 17, 1, 12, 5, 8, 193, 22, 25, 65, 29, 481, 1, 85, 1

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Cf. A003273, A006991, A062695, A259680-A259687.

More terms from Jinyuan Wang, Jan 01 2021

A259685 Let m = A062695(n); a(n) is value of b in decomposition of m defined in Comments.

Original entry on oeis.org

2, 4, 2, 56, 1, 2, 1, 1, 6, 1, 4, 4, 104, 2, 4, 1, 12, 4, 1, 8, 2, 6, 1, 2, 5, 1, 2, 204, 1, 2, 4, 1, 4, 3, 2, 1, 1, 12, 20, 3, 20, 4, 40, 3, 132, 6, 3, 2, 6, 2, 82, 17, 11, 4, 333, 14, 12, 6, 5, 2, 1, 52, 1, 12, 2, 29, 1, 1, 1972, 7, 24, 1504, 20, 360, 10, 2952

Offset: 1

N. J. A. Sloane, Jul 04 2015

nonn

Let m = A062695(n). Write m*y^2 = x^3 - x as m*square = A*B*(A-B)*(A+B) where A and B are the numerator and denominator of x. Then A, B, A-B, A+B have the form s*a^2, t*b^2, u*c^2, v*d^2 for some decomposition of m as s*t*u*v and some natural numbers a,b,c,d. These eight numbers are given in A259680-A259687.

G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340.
G. Kramarz, All congruent numbers less than 2000, Math. Annalen, 273 (1986), 337-340. [Annotated, corrected, scanned copy]

Cf. A003273, A006991, A062695, A259680-A259687.

More terms from Jinyuan Wang, Jan 01 2021

cp's OEIS Frontend

A248401 Noncongruent squarefree numbers n with A248394(n)/d(n) = 3, where d(n) = A000005(n).

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A248402 Noncongruent squarefree numbers n with A248394(n)/d(n) = -3, where d(n) = A000005(n).

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A248403 Noncongruent squarefree numbers n with A248395(n)/d(n) = 1, where d(n) = A000005(n).

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A248404 Noncongruent squarefree numbers n with A248395(n)/d(n) = -1, where d(n) = A000005(n).

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A248405 Noncongruent squarefree numbers n with A248395(n)/d(n) = 2, where d(n) = A000005(n).

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A259681 Let m = A062695(n); a(n) is value of t in decomposition of m defined in Comments.

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A259682 Let m = A062695(n); a(n) is value of u in decomposition of m defined in Comments.

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A259683 Let m = A062695(n); a(n) is value of v in decomposition of m defined in Comments.

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Extensions

A259684 Let m = A062695(n); a(n) is value of a in decomposition of m defined in Comments.

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Extensions

A259685 Let m = A062695(n); a(n) is value of b in decomposition of m defined in Comments.

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