Displaying 1-10 of 16 results found.
Numbers that are the sum of 2 squares.
(Formerly M0968 N0361)
+10
232
0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 34, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 65, 68, 72, 73, 74, 80, 81, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 125, 128, 130, 136, 137, 144, 145, 146, 148, 149, 153, 157, 160
Least number of squares that add up to n.
(Formerly M0404 N0155)
+10
91
0, 1, 2, 3, 1, 2, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 3, 1, 2, 3, 4, 2, 3, 4, 2, 3, 2, 3, 1, 2, 3, 4, 2, 2, 3, 3, 3, 2, 3, 4, 3, 1, 2, 3, 2, 2, 3, 4, 3, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 3, 2, 3, 3, 4, 2, 2, 2, 3, 3, 3, 3, 4, 2, 1, 2, 3, 3, 2, 3, 4, 3, 2, 2, 3, 4, 3, 3, 4, 3, 2, 2, 3, 1, 2, 3, 4, 2, 3
Numbers that are not the sum of 2 squares.
+10
59
3, 6, 7, 11, 12, 14, 15, 19, 21, 22, 23, 24, 27, 28, 30, 31, 33, 35, 38, 39, 42, 43, 44, 46, 47, 48, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67, 69, 70, 71, 75, 76, 77, 78, 79, 83, 84, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 102, 103, 105, 107, 108, 110, 111, 112, 114, 115, 118, 119, 120, 123, 124, 126, 127, 129, 131, 132, 133, 134, 135, 138, 139, 140, 141, 142, 143, 147, 150, 151, 152, 154, 155, 156, 158, 159, 161, 163, 165, 166, 167, 168, 171, 172, 174, 175, 176, 177, 179, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 195, 198, 199
Sums of three squares: numbers of the form x^2 + y^2 + z^2.
+10
56
0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83
Nonsquare positive integers n such that the fundamental unit of quadratic field Q(sqrt(n)) has norm -1.
+10
18
2, 5, 8, 10, 13, 17, 18, 20, 26, 29, 32, 37, 40, 41, 45, 50, 52, 53, 58, 61, 65, 68, 72, 73, 74, 80, 82, 85, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 122, 125, 128, 130, 137, 145, 148, 149, 153, 157, 160, 162, 164, 170, 173, 180, 181, 185, 193, 197, 200
Numbers that are the sum of 3 but no fewer nonzero squares.
+10
11
3, 6, 11, 12, 14, 19, 21, 22, 24, 27, 30, 33, 35, 38, 42, 43, 44, 46, 48, 51, 54, 56, 57, 59, 62, 66, 67, 69, 70, 75, 76, 77, 78, 83, 84, 86, 88, 91, 93, 94, 96, 99, 102, 105, 107, 108, 110, 114, 115, 118, 120, 123, 126, 129, 131, 132, 133, 134, 138, 139, 140, 141, 142
Numbers n that are the product of two distinct odd primes and x^2 + y^2 = n has integer solutions.
+10
9
65, 85, 145, 185, 205, 221, 265, 305, 365, 377, 445, 481, 485, 493, 505, 533, 545, 565, 629, 685, 689, 697, 745, 785, 793, 865, 901, 905, 949, 965, 985, 1037, 1073, 1145, 1157, 1165, 1189, 1205, 1241, 1261, 1285, 1313, 1345, 1385, 1405, 1417, 1465, 1469
a(n) is the least k such that there are exactly n distinct numbers j that can be expressed as the sum of two squares with k^2 < j < (k+1)^2, or -1 if such a k does not exist.
+10
8
0, 1, 2, 4, 5, 7, 8, 10, 13, 12, 15, 17, 19, 23, 21, 24, 25, 28, 32, 31, 34, 37, 39, 44, 41, 43, 45, 50, 51, 48, 57, 55, 56, 59, 64, 63, 68, 69, 74, 77, 78, 75, 72, 80, 88, 84, -1, 94, 89, 96, 93, 99, 97, 102, 108, -1, 106, 111, 110, 113, 117, 120, -1, 123, 133, 127, 130, 137, 142, 138, 139, -1, 135
Square numbers which are sums of 2 distinct nonzero squares.
+10
6
25, 100, 169, 225, 289, 400, 625, 676, 841, 900, 1156, 1225, 1369, 1521, 1600, 1681, 2025, 2500, 2601, 2704, 2809, 3025, 3364, 3600, 3721, 4225, 4624, 4900, 5329, 5476, 5625, 6084, 6400, 6724, 7225, 7569, 7921, 8100, 8281, 9025, 9409, 10000, 10201
Number of positive integers below 10^n, excluding perfect squares, which have a representation as a sum of 2 positive squares.
+10
6
3, 33, 298, 2649, 23711, 215341, 1982296, 18447847, 173197435, 1637524156, 15570196516, 148735628858, 1426303768587, 13722207893214, 132387231596281, 1280309591127436
FORMULA
a(n) = |{ 0<k<10^n : k in { A000415} }|.
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