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Search: a125013 -id:a125013
Displaying 1-10 of 12 results found. page 1 2
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A125007 Numbers n for which no nontrivial positive magic squares with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005. +10
14
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 35, 37, 40, 41, 43, 44, 47, 49, 52, 53, 55, 56, 59, 61, 64, 67, 68, 71, 73, 76, 77, 79, 83, 88, 89, 91, 92, 97, 101, 103, 104, 107, 109, 112, 113, 116, 119, 121, 124, 127, 128, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A125007 lists all values s such that A125005(s) = 0.
LINKS
Table of n, a(n) for n=1..69.
EXAMPLE
Since there exists a nontrivial positive magic square with magic sum 15, 15 is not a value of A125007.
CROSSREFS
Cf. A125005, A125006, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,42
LINKS
Table of n, a(n) for n=1..105.
EXAMPLE
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.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125008 lists all values s such that A125005(s) = 1.
LINKS
Table of n, a(n) for n=1..61.
CROSSREFS
Cf. A125005, A125006, A125007, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125009 lists all values s such that A125005(s) = 2.
LINKS
Table of n, a(n) for n=1..53.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125010 lists all values s such that A125005(s) = 3.
LINKS
Table of n, a(n) for n=1..52.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125011 lists all values s such that A125005(s) = 4.
LINKS
Table of n, a(n) for n=1..47.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125012 lists all values s such that A125005(s) = 5.
LINKS
Table of n, a(n) for n=1..44.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125014 lists all values s such that A125005(s) = 7.
LINKS
Table of n, a(n) for n=1..42.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125015 lists all values s such that A125005(s) = 8.
LINKS
Table of n, a(n) for n=1..42.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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. +10
13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A125016 lists all values s such that A125005(s) = 9.
LINKS
Table of n, a(n) for n=1..35.
CROSSREFS
Cf. A125005, A125006, A125007, A125008, A125009, A125010, A125011, A125012, A125013, A125014, A125015, A125016, A125017.
KEYWORD
easy,nonn
AUTHOR
Jens Voß, Nov 15 2006
STATUS
approved
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Last modified August 29 11:15 EDT 2024. Contains 375512 sequences. (Running on oeis4.)