cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A290503 Hypotenuses for which there exist exactly 15 distinct integer triangles.

Original entry on oeis.org

30517578125, 61035156250, 91552734375, 122070312500, 183105468750, 213623046875, 244140625000, 274658203125, 335693359375, 366210937500, 427246093750, 488281250000, 549316406250, 579833984375, 640869140625, 671386718750, 701904296875, 732421875000
Offset: 1

Views

Author

Hamdi Sahloul, Aug 04 2017

Keywords

Comments

Numbers whose square is decomposable in 15 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity fifteen.

Examples

			a(1) = 30517578125 = 5^15, a(5) = 183105468750 = 2*3*5^15, a(101) = 5859375000000 = 2^6*3*5^15.

Links

Crossrefs

Cf. A002144, A006339, A046080, A046109, A083025.
Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A097238 (16), A097239 (17), A290504 (18), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Programs

  • Mathematica
    r[a_]:={b, c}/.{ToRules[Reduce[0Vincenzo Librandi, Mar 01 2016 *)

Formula

Terms are obtained by the product A004144(k)*A002144(p)^15 for k, p > 0 ordered by increasing values.

A290504 Hypotenuses for which there exist exactly 18 distinct integer triangles.

Original entry on oeis.org

3814697265625, 7629394531250, 11444091796875, 15258789062500, 22888183593750, 26702880859375, 30517578125000, 34332275390625, 41961669921875, 45776367187500, 53405761718750, 61035156250000, 68664550781250, 72479248046875, 80108642578125, 83923339843750
Offset: 1

Views

Author

Hamdi Sahloul, Aug 04 2017

Keywords

Comments

Numbers whose square is decomposable in 18 different ways into the sum of two nonzero squares: these are those with only one prime divisor of the form 4k+1 with multiplicity eighteen.

Examples

			a(1) = 3814697265625 = 5^18, a(5) = 22888183593750 = 2*3*5^18, a(101) = 732421875000000 = 2^6*3*5^18.

Links

Crossrefs

Cf. A002144, A006339, A046080, A046109, A083025.
Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290505 (19), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Programs

  • Mathematica
    r[a_]:={b, c}/.{ToRules[Reduce[0Vincenzo Librandi, Mar 01 2016 *)

Formula

Terms are obtained by the product A004144(k)*A002144(p)^18 for k, p > 0 ordered by increasing values.

A290505 Hypotenuses for which there exist exactly 19 distinct integer triangles.

Original entry on oeis.org

203125, 265625, 406250, 453125, 531250, 578125, 609375, 640625, 796875, 812500, 828125, 906250, 953125, 1062500, 1140625, 1156250, 1218750, 1281250, 1359375, 1390625, 1421875, 1515625, 1578125, 1593750, 1625000, 1656250, 1703125, 1734375, 1765625, 1812500
Offset: 1

Views

Author

Hamdi Sahloul, Aug 04 2017

Keywords

Comments

Numbers whose square is decomposable in 19 different ways into the sum of two nonzero squares: these are those with exactly two distinct prime divisors of the form 4k+1 with one, and six respective multiplicities, or with only one prime divisor of this form with multiplicity nineteen.

Examples

			a(1) = 203125 = 5^6*13, a(5) = 531250 = 2*5^6*17, a(281) = 12796875 = 3^2*5^6*7*13.

Links

Crossrefs

Cf. A002144, A006339, A046080, A046109, A083025.
Cf. A004144 (0), A084645 (1), A084646 (2), A084647 (3), A084648 (4), A084649 (5), A097219 (6), A097101 (7), A290499 (8), A290500 (9), A097225 (10), A290501 (11), A097226 (12), A097102 (13), A290502 (14), A290503 (15), A097238 (16), A097239 (17), A290504 (18), A097103 (22), A097244 (31), A097245 (37), A097282 (40), A097626 (67).

Programs

  • Mathematica
    r[a_]:={b, c}/.{ToRules[Reduce[0Vincenzo Librandi, Mar 01 2016 *)

Formula

Terms are obtained by the products A004144(k)*A002144(p1)*A002144(p2)^6, or A004144(k)*A002144(p1)^19 for k, p1, p2 > 0 ordered by increasing values.
Previous Showing 21-23 of 23 results.

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