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 1-7 of 7 results.

A343967 Numbers that are the sum of three positive cubes in five or more ways.

Original entry on oeis.org

161568, 262683, 314712, 326808, 359568, 443197, 444536, 471960, 503208, 513729, 515376, 526023, 529199, 532683, 552824, 597960, 702729, 736371, 746992, 806688, 844416, 863379, 907479, 924048, 931419, 975213, 1011067, 1028663, 1062937, 1092853, 1152152, 1172016, 1211048, 1232496, 1258011
Offset: 1

Views

Author

David Consiglio, Jr., May 05 2021

Keywords

Examples

			314712 =  4^3 +  6^3 + 68^3
       =  5^3 + 24^3 + 67^3
       =  6^3 + 30^3 + 66^3
       = 31^3 + 41^3 + 60^3
       = 36^3 + 48^3 + 54^3
so 314712 is a term of this sequence.

Links

Crossrefs

Cf. A025333, A051167, A343968, A343970, A343987, A344364, A345083.

Programs

  • 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(1,50)]
for pos in cwr(power_terms,3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 5])
for x in range(len(rets)):
    print(rets[x])

A343971 Numbers that are the sum of four positive cubes in four or more ways.

Original entry on oeis.org

1979, 2737, 3663, 4384, 4445, 4474, 4949, 5105, 5131, 5257, 5320, 5473, 5499, 5553, 5616, 5733, 5768, 5833, 5852, 5859, 6064, 6104, 6328, 6372, 6435, 6587, 6643, 6832, 6883, 6912, 6974, 7000, 7030, 7120, 7217, 7371, 7560, 7686, 7777, 7840, 8099, 8108, 8281, 8316, 8344, 8379, 8414, 8505, 8568, 8927, 9016, 9018
Offset: 1

Views

Author

David Consiglio, Jr., May 05 2021

Keywords

Examples

			3663 = 1^3 + 10^3 + 11^3 + 11^3
     = 2^3 +  4^3 +  6^3 + 15^3
     = 2^3 +  9^3 +  9^3 + 13^3
     = 4^3 +  7^3 +  8^3 + 14^3
so 3663 is a term.

Links

Crossrefs

Cf. A025369, A025407, A343968, A343972, A343987, A344034, A344352.

Programs

  • 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(1,50)]
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
    print(rets[x])

A343989 Numbers that are the sum of five positive cubes in five or more ways.

Original entry on oeis.org

1765, 1980, 2043, 2104, 2195, 2250, 2430, 2449, 2486, 2491, 2493, 2547, 2584, 2592, 2738, 2745, 2764, 2817, 2888, 2915, 2953, 2969, 2979, 3095, 3096, 3133, 3142, 3186, 3188, 3214, 3240, 3249, 3275, 3277, 3310, 3312, 3366, 3403, 3422, 3459, 3464, 3466, 3483, 3492, 3520, 3529, 3583, 3608, 3627, 3653, 3664, 3671
Offset: 1

Views

Author

David Consiglio, Jr., May 06 2021

Keywords

Examples

			2043 = 1^3 + 4^3 + 5^3 +  5^3 + 12^3
     = 2^3 + 2^3 + 3^3 + 10^3 + 10^3
     = 2^3 + 3^3 + 4^3 +  6^3 + 12^3
     = 4^3 + 5^3 + 5^3 +  9^3 + 10^3
     = 4^3 + 6^3 + 6^3 +  6^3 + 11^3
so 2043 is a term.

Links

Crossrefs

Cf. A343987, A343988, A344034, A344358, A344798, A345174, A345514.

Programs

  • 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(1,50)]
for pos in cwr(power_terms,5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 5])
for x in range(len(rets)):
    print(rets[x])

A345148 Numbers that are the sum of four third powers in six or more ways.

Original entry on oeis.org

6883, 12411, 13104, 13923, 14112, 14581, 14896, 14904, 15561, 15876, 16317, 16640, 17208, 17479, 17992, 18739, 18865, 18928, 19035, 19080, 19376, 19665, 19712, 19763, 19880, 20007, 20384, 20755, 20979, 21203, 21231, 21420, 21707, 21896, 22409, 22617, 22743
Offset: 1

Views

Author

David Consiglio, Jr., Jun 09 2021

Keywords

Examples

			6883 is a term because 6883 = 2^3 + 2^3 + 2^3 + 18^3  = 2^3 + 4^3 + 14^3 + 14^3  = 3^3 + 7^3 + 7^3 + 17^3  = 3^3 + 10^3 + 13^3 + 13^3  = 4^3 + 10^3 + 10^3 + 15^3  = 7^3 + 8^3 + 8^3 + 16^3.

Links

Crossrefs

Cf. A025371, A343987, A344904, A345083, A345149, A345150, A345174.

Programs

  • 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)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 6])
for x in range(len(rets)):
    print(rets[x])

A343986 Numbers that are the sum of four positive cubes in exactly five ways.

Original entry on oeis.org

5105, 5131, 5616, 5859, 6435, 7777, 9315, 9737, 9793, 10017, 10250, 10458, 10936, 10962, 11000, 11060, 11088, 11592, 11664, 11781, 12168, 12229, 12285, 12320, 12385, 12392, 12707, 13384, 13734, 13832, 13904, 14183, 14239, 14833, 15176, 15596, 15624, 15752, 15759, 15778, 16093, 16289, 16354, 16480, 16569
Offset: 1

Views

Author

David Consiglio, Jr., May 06 2021

Keywords

Comments

Differs from A343987 at term 6 because 6883 = 2^3 + 2^3 + 2^3 + 19^3 = 2^3 + 5^3 + 15^3 + 15^3 = 3^3 + 8^3 + 8^3 + 18^3 = 4^3 + 11^3 + 14^3 + 14^3 = 5^3 + 11^3 + 11^3 + 16^3 = 8^3 + 9^3 + 9^3 + 17^3.

Examples

			5616 is a term because 5616 = 1^3 + 8^3 + 12^3 + 15^3 = 2^3 + 8^3 + 10^3 + 16^3 = 4^3 + 4^3 + 14^3 + 14^3 = 4^3 + 5^3 + 11^3 + 16^3 = 8^3 + 9^3 + 10^3 + 15^3.

Links

Crossrefs

Cf. A025361, A343970, A343972, A343987, A343988, A344357, A345149.

Programs

  • 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(1,50)]
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 5])
for x in range(len(rets)):
    print(rets[x])

A344356 Numbers that are the sum of four fourth powers in five or more ways.

Original entry on oeis.org

2147874, 2266338, 2690658, 3189603, 3464178, 3754674, 3847554, 4030419, 4165794, 4457298, 4884114, 5229378, 5624739, 5978883, 5980178, 5981283, 6014178, 6044418, 6134994, 6258723, 6313953, 6400194, 6576339, 6593538, 6612354, 6899603, 7088898, 7498323, 7811874, 7918498, 8064018, 8292323
Offset: 1

Views

Author

David Consiglio, Jr., May 15 2021

Keywords

Examples

			2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.

Links

Crossrefs

Cf. A343987, A344352, A344357, A344358, A344364, A344904.

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, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 5])
for x in range(len(rets)):
    print(rets[x])

A025370 Numbers that are the sum of 4 nonzero squares in 5 or more ways.

Original entry on oeis.org

82, 90, 100, 102, 103, 106, 108, 111, 114, 115, 117, 118, 122, 124, 126, 127, 130, 132, 133, 135, 138, 143, 145, 147, 148, 150, 151, 153, 154, 156, 157, 159, 162, 163, 165, 166, 167, 169, 170, 171, 172, 174, 175, 177, 178, 180, 181, 182, 183, 186, 187, 188, 189, 190
Offset: 1

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

Cf. A025333, A025361, A025369, A025371, A343987, A344798.

Formula

{n: A025428(n) >= 5}. Union of A025371 and A025361. - R. J. Mathar, Jun 15 2018
Showing 1-7 of 7 results.

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

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