A124982 -id:A124982 - cp's OEIS frontend

A125022 Numbers with a unique partition as the sum of 2 squares x^2 + y^2.

0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 26, 29, 32, 34, 36, 37, 40, 41, 45, 49, 52, 53, 58, 61, 64, 68, 72, 73, 74, 80, 81, 82, 89, 90, 97, 98, 101, 104, 106, 109, 113, 116, 117, 121, 122, 128, 136, 137, 144, 146, 148, 149, 153, 157, 160, 162, 164, 173, 178, 180, 181

Offset: 1

Artur Jasinski, Nov 16 2006

nonn

A000161(a(n)) = 1. [Reinhard Zumkeller, Aug 16 2011]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A002145, A124982, A125021, A034026.

Cf. A025284, A081324, A022544, A001481, A118882.

import Data.List (elemIndices)
a125022 n = a125022_list !! (n-1)
a125022_list = elemIndices 1 a000161_list
-- Reinhard Zumkeller, Aug 16 2011

Select[Range[0,200],Length@PowersRepresentations[#,2,2]==1&] (* Giorgos Kalogeropoulos, Mar 21 2021 *)

a(n) = A125021(n)/2.

Name edited by Giorgos Kalogeropoulos, Mar 21 2021

A124983 Nonprime numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.

Original entry on oeis.org

1, 9, 45, 49, 81, 117, 121, 153, 245, 261, 333, 361, 369, 405, 441, 477, 529, 549, 605, 637, 657, 729, 801, 833, 873, 909, 961, 981, 1017, 1053, 1089, 1233, 1341, 1377, 1413, 1421, 1557, 1573, 1629, 1737, 1773, 1805, 1813, 1849, 2009, 2057, 2061, 2097, 2169

Offset: 1

Artur Jasinski, Nov 16 2006

nonn

Intersection of A124982 and A125018. - Michel Marcus, Nov 02 2013

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000161, A002145, A124982, A125018, A125020.

Select[4 * Range[0, 500] + 1, !PrimeQ[#] && Length @ PowersRepresentations[#, 2, 2] == 1 &] (* Amiram Eldar, Mar 12 2020 *)

isok(n)= {if (isprime(n) || (n % 4 != 1), return (0)); A000161(n) == 1;} \\ Michel Marcus, Nov 02 2013

More terms from Michel Marcus, Nov 02 2013

A125018 Numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.

Original entry on oeis.org

1, 5, 9, 13, 17, 29, 37, 41, 45, 49, 53, 61, 73, 81, 89, 97, 101, 109, 113, 117, 121, 137, 149, 153, 157, 173, 181, 193, 197, 229, 233, 241, 245, 257, 261, 269, 277, 281, 293, 313, 317, 333, 337, 349, 353, 361, 369, 373, 389, 397, 401, 405, 409, 421, 433

Offset: 1

Artur Jasinski, Nov 16 2006

nonn

			5 = 1^2 + 2^2, 9 = 0^2 + 3^2, 13 = 2^2 + 3^2, 17 = 1^2 + 4^2, 29 = 2^2 + 5^2, ... - _Michael Somos_, Jul 25 2023

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002145, A119345, A124982, A124983.

Select[4 * Range[0, 100] + 1, Length @ PowersRepresentations[#, 2, 2] == 1 &] (* Amiram Eldar, Mar 12 2020 *)

isok(n)= {if (n % 4 != 1, return(0)); A000161(n) == 1;} \\ Michel Marcus, Nov 02 2013

More terms from Michel Marcus, Nov 02 2013

A125020 a(n) = (A124983(n)-1)/4.

Original entry on oeis.org

0, 2, 11, 12, 20, 29, 30, 38, 61, 65, 83, 90, 92, 101, 110, 119, 132, 137, 151, 159, 164, 182, 200, 208, 218, 227, 240, 245, 254, 263, 272, 308, 335, 344, 353, 355, 389, 393, 407, 434, 443, 451, 453, 462, 502, 514, 515, 524, 542, 551, 552, 578, 587, 600, 605, 623

Offset: 1

Artur Jasinski, Nov 16 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A124983, A002145, A124982, A124983.

Select[Range[0, 600], !PrimeQ[4*# + 1] && Length @ PowersRepresentations[4*# + 1, 2, 2] == 1 &] (* Amiram Eldar, Mar 12 2020 *)

More terms from Amiram Eldar, Mar 12 2020

A125021 Even numbers with a unique partition as the sum of 2 squares x^2 + y^2.

Original entry on oeis.org

0, 2, 4, 8, 10, 16, 18, 20, 26, 32, 34, 36, 40, 52, 58, 64, 68, 72, 74, 80, 82, 90, 98, 104, 106, 116, 122, 128, 136, 144, 146, 148, 160, 162, 164, 178, 180, 194, 196, 202, 208, 212, 218, 226, 232, 234, 242, 244, 256, 272, 274, 288, 292, 296, 298, 306, 314

Offset: 1

Artur Jasinski, Nov 16 2006, corrected Nov 18 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A002145, A124982, A125022.

Select[2 * Range[0, 200], Length @ PowersRepresentations[#, 2, 2] == 1 &] (* Amiram Eldar, Mar 12 2020 *)

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A125022 Numbers with a unique partition as the sum of 2 squares x^2 + y^2.

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A124983 Nonprime numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.

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A125018 Numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.

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A125020 a(n) = (A124983(n)-1)/4.

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A125021 Even numbers with a unique partition as the sum of 2 squares x^2 + y^2.

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