A343986 -id:A343986 - cp's OEIS frontend

A343987 Numbers that are the sum of four positive cubes in five or more ways.

5105, 5131, 5616, 5859, 6435, 6883, 7777, 9315, 9737, 9793, 10017, 10250, 10458, 10936, 10962, 11000, 11060, 11088, 11592, 11664, 11781, 12168, 12229, 12285, 12320, 12385, 12392, 12411, 12707, 13104, 13384, 13734, 13832, 13904, 13923, 14112, 14183, 14239, 14581, 14833, 14896, 14904, 15176, 15561, 15596

Offset: 1

David Consiglio, Jr., May 06 2021

nonn

			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
so 5616 is a term.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A025370, A343967, A343971, A343986, A343989, A344356, A345148.

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], end=", ")

A343972 Numbers that are the sum of four positive cubes in exactly four ways.

Original entry on oeis.org

1979, 2737, 3663, 4384, 4445, 4474, 4949, 5257, 5320, 5473, 5499, 5553, 5733, 5768, 5833, 5852, 6064, 6104, 6328, 6372, 6587, 6643, 6832, 6912, 6974, 7000, 7030, 7120, 7217, 7371, 7560, 7686, 7840, 8099, 8108, 8281, 8316, 8344, 8379, 8414, 8505, 8568, 8927, 9016, 9018, 9044, 9072, 9100, 9289, 9548, 9648, 9800

Offset: 1

David Consiglio, Jr., May 05 2021

nonn

This sequence varies from A343971 at term 8 because 5105 = 1^3 + 1^3 + 12^3 + 15^3 = 1^3 + 2^3 + 10^3 + 16^3 = 1^3 + 9^3 + 10^3 + 15^3 = 4^3 + 4^3 + 4^3 + 17^3 = 4^3 + 6^3 + 9^3 + 16^3.

			3663 is a term because 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.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A025360, A025405, A343969, A343971, A343986, A344035, A344353.

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])

A343988 Numbers that are the sum of five positive cubes in exactly five ways.

Original entry on oeis.org

1765, 1980, 2043, 2104, 2195, 2250, 2449, 2486, 2491, 2493, 2547, 2584, 2592, 2738, 2745, 2764, 2817, 2888, 2915, 2953, 2969, 3095, 3096, 3133, 3142, 3186, 3188, 3240, 3275, 3277, 3310, 3366, 3403, 3422, 3459, 3464, 3466, 3483, 3529, 3583, 3608, 3627, 3653, 3664, 3671, 3690, 3697, 3707, 3725, 3744, 3746, 3781

Offset: 1

David Consiglio, Jr., May 06 2021

nonn

Differs from A343989 at term 7 because 2430 = 1^3 + 2^3 + 2^3 + 6^3 + 13^3 = 1^3 + 4^3 + 5^3 + 8^3 + 12^3 = 2^3 + 2^3 + 7^3 + 7^3 + 12^3 = 2^3 + 3^3 + 4^3 + 10^3 + 11^3 = 3^3 + 6^3 + 9^3 + 9^3 + 9^3 = 4^3 + 5^3 + 8^3 + 9^3 + 10^3.

			2043 is a term because 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.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A294739, A343986, A343989, A344035, A344359, A345175, A345767.

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])

A344357 Numbers that are the sum of four fourth powers in exactly five ways.

Original entry on oeis.org

2147874, 2266338, 2690658, 3189603, 3464178, 3754674, 4030419, 4165794, 4457298, 4884114, 5229378, 5978883, 5980178, 5981283, 6014178, 6134994, 6258723, 6313953, 6400194, 6612354, 7088898, 7498323, 7811874, 7918498, 8064018, 8292323, 8630259, 9146034, 9269523, 9388978, 9397683, 9726978

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

Differs from A344356 at term 7 because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.

			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.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A343986, A344353, A344356, A344359, A344365, A344921.

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])

A345149 Numbers that are the sum of four third powers in exactly six ways.

Original entry on oeis.org

6883, 12411, 13923, 14112, 14581, 14896, 14904, 15561, 15876, 16317, 16640, 17208, 17479, 17992, 18739, 18865, 19035, 19080, 19665, 19712, 19763, 19880, 20007, 20384, 20979, 21231, 21420, 21707, 22409, 22617, 23149, 23940, 24355, 25515, 25984, 26208, 26334

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345148 at term 3 because 13104 = 1^3 + 10^3 + 16^3 + 18^3 = 1^3 + 11^3 + 14^3 + 19^3 = 2^3 + 9^3 + 15^3 + 19^3 = 4^3 + 6^3 + 14^3 + 20^3 = 4^3 + 9^3 + 10^3 + 21^3 = 5^3 + 7^3 + 11^3 + 21^3 = 8^3 + 9^3 + 14^3 + 19^3.

			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.

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Cf. A025362, A343986, A344921, A345084, A345148, A345151, A345175.

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])

A343970 Numbers that are the sum of three positive cubes in exactly five 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

David Consiglio, Jr., May 05 2021

nonn

This sequence differs from A343967 at term 40 because 1296378 = 3^3 + 76^3 + 95^3 = 9^3 + 33^3 + 108^3 = 21^3 + 77^3 + 94^3 = 31^3 + 59^3 + 102^3 = 33^3 + 81^3 + 90^3 = 60^3 + 75^3 + 87^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Cf. A025325, A343967, A343969, A343986, A344365, A345084.

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])

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A343987 Numbers that are the sum of four positive cubes in five or more ways.

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A343972 Numbers that are the sum of four positive cubes in exactly four ways.

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A343988 Numbers that are the sum of five positive cubes in exactly five ways.

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A344357 Numbers that are the sum of four fourth powers in exactly five ways.

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A345149 Numbers that are the sum of four third powers in exactly six ways.

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A343970 Numbers that are the sum of three positive cubes in exactly five ways.

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