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.

Showing 1-10 of 13 results. Next

A125005 Numbers of orders of nontrivial positive magic-squares with magic sum n. A nontrivial positive magic square is a k-by-k array of consecutive positive integers (not necessarily including 1) such that all rows, all columns and the two diagonals each add up to the same constant (the "magic sum"), with the additional restriction that k (the "order") is greater than 1.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 3, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 2
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Examples

			A125005(15)=1 because there is exactly one order k > 1 (namely k = 3) such that there exists a magic square of order k having the magic sum 15. By adding 1 to each table cell of one such magic square, a magic square with magic sum 18 is obtained, hence A125005(18) = 1 as well.

Crossrefs

Cf. A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

A125008 Numbers n for which nontrivial positive magic squares of exactly one order with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

15, 18, 21, 24, 27, 30, 33, 34, 36, 38, 39, 45, 46, 48, 50, 51, 57, 58, 60, 62, 63, 65, 69, 72, 74, 80, 81, 82, 84, 85, 86, 87, 93, 94, 95, 96, 98, 99, 100, 106, 108, 115, 118, 122, 125, 132, 134, 140, 142, 144, 145, 146, 154, 155, 156, 158, 160, 166, 168, 178, 185
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125008 lists all values s such that A125005(s) = 1.

Crossrefs

Cf. A125005, A125006, A125007, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

A125009 Numbers n for which nontrivial positive magic squares of exactly 2 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

42, 54, 66, 70, 75, 78, 102, 105, 110, 111, 114, 117, 120, 123, 126, 129, 130, 138, 141, 147, 153, 159, 162, 170, 171, 174, 175, 177, 180, 182, 183, 186, 190, 198, 201, 207, 213, 219, 222, 230, 234, 237, 238, 240, 243, 245, 246, 249, 250, 252, 258, 260, 261
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125009 lists all values s such that A125005(s) = 2.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

A125010 Numbers n for which nontrivial positive magic squares of exactly 3 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

90, 135, 150, 165, 189, 195, 225, 231, 255, 270, 273, 285, 294, 300, 330, 345, 350, 357, 369, 375, 387, 390, 396, 399, 414, 423, 435, 459, 462, 465, 468, 477, 483, 486, 490, 504, 510, 513, 522, 531, 546, 549, 558, 570, 588, 594, 595, 603, 609, 612, 621, 639
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125010 lists all values s such that A125005(s) = 3.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

A125011 Numbers n for which nontrivial positive magic squares of exactly 4 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

210, 315, 378, 405, 420, 441, 450, 495, 540, 555, 567, 615, 645, 705, 756, 770, 795, 810, 819, 870, 885, 891, 900, 915, 918, 924, 930, 954, 966, 975, 1005, 1026, 1062, 1065, 1071, 1089, 1095, 1098, 1110, 1122, 1185, 1188, 1197, 1206, 1218, 1230, 1242
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125011 lists all values s such that A125005(s) = 4.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125012, A125013, A125014, A125015, A125016, A125017.

A125012 Numbers n for which nontrivial positive magic squares of exactly 5 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

525, 585, 630, 675, 693, 735, 765, 825, 855, 882, 1035, 1050, 1125, 1134, 1215, 1260, 1287, 1305, 1350, 1395, 1449, 1470, 1530, 1617, 1650, 1665, 1695, 1701, 1725, 1770, 1782, 1827, 1830, 1875, 1905, 1911, 1925, 1953, 1965, 2010, 2055, 2085, 2100, 2106
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125012 lists all values s such that A125005(s) = 5.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125013, A125014, A125015, A125016, A125017.

A125013 Numbers n for which nontrivial positive magic squares of exactly 6 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

945, 990, 1155, 1170, 1365, 1386, 1485, 1638, 1710, 1815, 1845, 1935, 1950, 1980, 2025, 2070, 2079, 2115, 2250, 2295, 2340, 2385, 2430, 2457, 2520, 2535, 2550, 2565, 2574, 2610, 2655, 2745, 2790, 2961, 3003, 3060, 3087, 3135, 3330, 3339, 3366, 3630
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125013 lists all values s such that A125005(s) = 6.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125014, A125015, A125016, A125017.

A125014 Numbers n for which nontrivial positive magic squares of exactly 7 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

1575, 1755, 1785, 1890, 1995, 2145, 2310, 2415, 2475, 2625, 2730, 2805, 2970, 3015, 3045, 3105, 3150, 3195, 3213, 3255, 3285, 3315, 3375, 3510, 3555, 3570, 3591, 3645, 3675, 3705, 3735, 3885, 3915, 3990, 4005, 4050, 4185, 4230, 4305, 4365, 4515, 4545
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125014 lists all values s such that A125005(s) = 7.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125015, A125016, A125017.

A125015 Numbers n for which nontrivial positive magic squares of exactly 8 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

2205, 2835, 2925, 3825, 4275, 4290, 4410, 4455, 4590, 4830, 4851, 4935, 4950, 5130, 5145, 5250, 5265, 5565, 5610, 5733, 5850, 6090, 6195, 6210, 6270, 6405, 6510, 6630, 6885, 7035, 7140, 7350, 7371, 7410, 7455, 7497, 7590, 7605, 7650, 7665, 7695, 7770
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125015 lists all values s such that A125005(s) = 8.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.

A125016 Numbers n for which nontrivial positive magic squares of exactly 9 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.

Original entry on oeis.org

5445, 5670, 6237, 6825, 7425, 7623, 8550, 8775, 10125, 10350, 10530, 10647, 10773, 11130, 11340, 11583, 12150, 12390, 12474, 12495, 12810, 12870, 13041, 13050, 13125, 13635, 13725, 13755, 13770, 13860, 13905, 14070, 14385, 14445, 14595
Offset: 1

Views

Author

Jens Voß, Nov 15 2006

Keywords

Comments

A125016 lists all values s such that A125005(s) = 9.

Crossrefs

Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
Showing 1-10 of 13 results. Next

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