Search: a011757 -id:a011757
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5, 16, 30, 44, 54, 76, 84, 108, 122, 120, 166, 182, 184, 234, 192, 260, 264, 294, 304, 342, 378, 342, 408, 426, 414, 468, 488, 474, 516, 576, 588, 576, 604, 590, 696, 694, 728, 694, 756, 828, 774, 776, 870, 862, 852, 1010, 922, 998, 916, 1020, 1032, 1110
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A001156
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Number of partitions of n into squares.
(Formerly M0221 N0079)
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+10
110
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1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 8, 9, 10, 10, 12, 13, 14, 14, 16, 19, 20, 21, 23, 26, 27, 28, 31, 34, 37, 38, 43, 46, 49, 50, 55, 60, 63, 66, 71, 78, 81, 84, 90, 98, 104, 107, 116, 124, 132, 135, 144, 154, 163, 169, 178, 192, 201, 209, 220, 235, 247, 256
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CROSSREFS
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Cf. A001462, A003114, A006141, A011757, A039900, A047993, A052335, A062457, A064174, A078135, A109298, A117144.
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A055875
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a(0)=1, a(n) = prime(n^3).
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+10
20
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1, 2, 19, 103, 311, 691, 1321, 2309, 3671, 5519, 7919, 10957, 14753, 19403, 24809, 31319, 38873, 47657, 57559, 69031, 81799, 96137, 112291, 130073, 149717, 171529, 195043, 220861, 248851, 279431, 312583, 347707, 386093, 427169, 470933, 517553
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A324588
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Heinz numbers of integer partitions of n into perfect squares (A001156).
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+10
11
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1, 2, 4, 7, 8, 14, 16, 23, 28, 32, 46, 49, 53, 56, 64, 92, 97, 98, 106, 112, 128, 151, 161, 184, 194, 196, 212, 224, 227, 256, 302, 311, 322, 343, 368, 371, 388, 392, 419, 424, 448, 454, 512, 529, 541, 604, 622, 644, 661, 679, 686, 736, 742, 776, 784, 827, 838
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COMMENTS
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Also products of elements of A011757.
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CROSSREFS
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Cf. A001156, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A118914, A276078.
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A123914
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a(n) = prime(n)^2 - prime(n^2). Commutator of (primes, squares) at n.
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+10
9
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2, 2, 2, -4, 24, 18, 62, 50, 110, 300, 300, 542, 672, 656, 782, 1190, 1602, 1578, 2052, 2300, 2246, 2780, 3086, 3710, 4772, 5150, 5090, 5442, 5400, 5772, 8556, 9000, 10032, 9980, 12270, 12174, 13328, 14520, 15146, 16430, 17714, 17660, 20604, 20502, 21200
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A324587
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Heinz numbers of integer partitions of n into distinct perfect squares (A033461).
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+10
8
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1, 2, 7, 14, 23, 46, 53, 97, 106, 151, 161, 194, 227, 302, 311, 322, 371, 419, 454, 541, 622, 661, 679, 742, 827, 838, 1009, 1057, 1082, 1193, 1219, 1322, 1358, 1427, 1589, 1619, 1654, 1879, 2018, 2114, 2143, 2177, 2231, 2386, 2437, 2438, 2741, 2854, 2933
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COMMENTS
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Also products of distinct elements of A011757.
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CROSSREFS
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Cf. A001156, A005117, A011757, A033461, A052335, A056239, A062457, A078135, A112798, A117144, A276078.
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A351982
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Number of integer partitions of n into prime parts with prime multiplicities.
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+10
8
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1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 3, 0, 1, 1, 3, 3, 3, 0, 1, 4, 5, 5, 3, 3, 5, 8, 5, 5, 6, 8, 8, 11, 7, 8, 10, 17, 14, 14, 12, 17, 17, 21, 18, 23, 20, 28, 27, 31, 27, 36, 32, 35, 37, 46, 41, 52, 45, 60, 58, 63, 59, 78, 71, 76, 81, 87, 80, 103, 107, 113, 114, 127
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A109770
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Prime(1^2) + prime(2^2) + ... + prime(n^2).
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+10
5
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2, 9, 32, 85, 182, 333, 560, 871, 1290, 1831, 2492, 3319, 4328, 5521, 6948, 8567, 10446, 12589, 15026, 17767, 20850, 24311, 28114, 32325, 36962, 42013, 47532, 53539, 60020, 67017, 74590, 82751, 91488, 100829, 110760, 121387, 132708, 144757
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2, 53, 419, 1619, 4637, 10627, 21391, 38873, 65687, 104729, 159521, 233879, 331943, 459341, 620201, 821641, 1069603, 1370099, 1731659, 2160553, 2667983, 3260137, 3948809, 4742977, 5653807, 6691987, 7867547, 9195889, 10688173, 12358069
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A323526
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One and prime numbers whose prime index is a perfect square.
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+10
4
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1, 2, 7, 23, 53, 97, 151, 227, 311, 419, 541, 661, 827, 1009, 1193, 1427, 1619, 1879, 2143, 2437, 2741, 3083, 3461, 3803, 4211, 4637, 5051, 5519, 6007, 6481, 6997, 7573, 8161, 8737, 9341, 9931, 10627, 11321, 12049, 12743, 13499, 14327, 15101, 15877, 16747, 17609
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FORMULA
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CROSSREFS
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Cf. A000290, A000720, A001248, A011757, A026478, A056239, A323520, A323521, A323525, A323527, A323528.
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