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 1-3 of 3 results.

A025395 Numbers that are the sum of 3 positive cubes in exactly 1 way.

Original entry on oeis.org

3, 10, 17, 24, 29, 36, 43, 55, 62, 66, 73, 80, 81, 92, 99, 118, 127, 129, 134, 136, 141, 153, 155, 160, 179, 190, 192, 197, 216, 218, 225, 232, 244, 253, 258, 270, 277, 281, 288, 307, 314, 342, 344, 345, 349, 352, 359, 368, 371, 375, 378, 397, 405, 408, 415, 433, 434, 440
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

A025456(a(n)) = 1. - Reinhard Zumkeller, Apr 23 2009

Links

Crossrefs

Cf. A003072, A024981, A025321, A025396, A025403, A338667, A344188.

Programs

  • Mathematica
    Reap[For[n = 1, n <= 500, n++, pr = Select[ PowersRepresentations[n, 3, 3], Times @@ # != 0 &]; If[pr != {} && Length[pr] == 1, Print[n, pr]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 31 2013 *)

A344187 Numbers that are the sum of two positive fourth powers in exactly one way.

Original entry on oeis.org

2, 17, 32, 82, 97, 162, 257, 272, 337, 512, 626, 641, 706, 881, 1250, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2592, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 4802, 5392, 6497, 6562, 6577, 6642, 6817, 7186, 7857, 8192, 8962, 10001, 10016, 10081, 10256, 10625, 10657, 11296, 12401, 13122, 14096, 14642
Offset: 1

Views

Author

David Consiglio, Jr., May 11 2021

Keywords

Comments

Differs from A003336 at term 11660 because 635318657 = 59^4 + 158^4 = 133^4 + 134^4

Examples

			32 is a member of this sequence because 32 = 2^4 + 2^4

Links

Crossrefs

Cf. A003336, A338667, A344188.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,50)]
for pos in cwr(power_terms,2):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

A343708 Numbers that are the sum of two positive cubes in exactly two ways.

Original entry on oeis.org

1729, 4104, 13832, 20683, 32832, 39312, 40033, 46683, 64232, 65728, 110656, 110808, 134379, 149389, 165464, 171288, 195841, 216027, 216125, 262656, 314496, 320264, 327763, 373464, 402597, 439101, 443889, 513000, 513856, 515375, 525824, 558441, 593047, 684019, 704977, 805688, 842751, 885248, 886464
Offset: 1

Views

Author

David Consiglio, Jr., Apr 26 2021

Keywords

Comments

This sequence differs from A001235 at term 455 because 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3 = A011541(3). Thus, this term is not in this sequence but is in A001235.

Examples

			13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.

Links

Crossrefs

Cf. A001235, A025285, A025396, A338667, A344804.

Programs

  • Mathematica
    Select[Range@70000,Length@Select[PowersRepresentations[#,2,3],FreeQ[#,0]&]==2&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)
  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1,1000)]#n
for pos in cwr(power_terms,2):#m
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 2])#s
for x in range(len(rets)):
    print(rets[x])
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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