A343971 -id:A343971 - cp's OEIS frontend

A343968 Numbers that are the sum of three positive cubes in four or more ways.

13896, 40041, 44946, 52200, 53136, 58995, 76168, 82278, 93339, 94184, 105552, 110683, 111168, 112384, 112832, 113400, 143424, 149416, 149904, 161568, 167616, 169560, 171296, 175104, 196776, 197569, 208144, 216126, 221696, 222984, 224505, 235808, 240813, 252062, 255312, 262683, 262781, 266031

Offset: 1

David Consiglio, Jr., May 05 2021

nonn

			44946 =  7^3 + 12^3 + 35^3
      =  9^3 + 17^3 + 34^3
      = 11^3 + 24^3 + 31^3
      = 16^3 + 17^3 + 33^3
so 44946 is a term.

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

Cf. A023051, A025332, A025398, A343967, A343969, A343971, A344277.

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 >= 4])
for x in range(len(rets)):
    print(rets[x])

A025407 Numbers that are the sum of 4 positive cubes in 3 or more ways.

Original entry on oeis.org

1225, 1521, 1582, 1584, 1738, 1764, 1979, 2009, 2249, 2366, 2415, 2422, 2457, 2459, 2485, 2520, 2539, 2737, 2753, 2763, 2790, 2799, 3008, 3094, 3185, 3187, 3213, 3248, 3276, 3392, 3456, 3458, 3465, 3572, 3582, 3600, 3607, 3626, 3656, 3663, 3717, 3736

Offset: 1

David W. Wilson

nonn

Cf. A025368, A025398, A025405, A025406, A343704, A343971, A344241.

{n: A025457(n) >= 3}. - R. J. Mathar, Jun 15 2018

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

Original entry on oeis.org

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=", ")

A344034 Numbers that are the sum of five positive cubes in four or more ways.

Original entry on oeis.org

1252, 1376, 1461, 1522, 1548, 1585, 1590, 1646, 1702, 1709, 1737, 1739, 1765, 1772, 1798, 1802, 1810, 1864, 1889, 1954, 1980, 1987, 2006, 2033, 2043, 2081, 2096, 2104, 2152, 2160, 2195, 2225, 2241, 2250, 2251, 2276, 2313, 2322, 2339, 2341, 2367, 2374, 2377, 2416, 2423, 2430, 2449, 2456, 2458, 2465, 2467, 2486

Offset: 1

David Consiglio, Jr., May 07 2021

nonn

			1461 = 1^3 + 1^3 + 1^3 + 9^3 +  9^3
     = 1^3 + 1^3 + 4^3 + 4^3 + 11^3
     = 3^3 + 3^3 + 4^3 + 7^3 + 10^3
     = 6^3 + 6^3 + 7^3 + 7^3 +  7^3
so 1461 is a term of this sequence.

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

Cf. A343704, A343971, A343989, A344035, A344354, A344797, A345513.

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 >= 4])
for x in range(len(rets)):
    print(rets[x])

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])

A344352 Numbers that are the sum of four fourth powers in four or more ways.

Original entry on oeis.org

236674, 282018, 300834, 334818, 478338, 637794, 650034, 650658, 708483, 708834, 729938, 789378, 816578, 832274, 849954, 941859, 989043, 1042083, 1045539, 1099203, 1099458, 1102258, 1179378, 1243074, 1257954, 1283874, 1323234, 1334979, 1339074, 1342979, 1352898, 1357059, 1379043, 1518578

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

			300834 is a term of this sequence because 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.

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

Cf. A343971, A344241, A344277, A344353, A344354, A344356.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1,200)]
count = 1
for pos in cwr(power_terms,4):
    tot = sum(pos)
    keep[tot] += 1
    count += 1
rets = sorted([k for k,v in keep.items() if v >= 4])
for x in range(len(rets)):
    print(rets[x])

A025369 Numbers that are the sum of 4 nonzero squares in 4 or more ways.

Original entry on oeis.org

52, 58, 63, 70, 76, 82, 84, 87, 90, 91, 93, 97, 98, 100, 102, 103, 105, 106, 108, 111, 114, 115, 117, 118, 119, 122, 123, 124, 126, 127, 130, 132, 133, 135, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 150, 151, 153, 154, 155, 156, 157, 158, 159, 162, 163, 165, 166

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025332, A025360, A025368, A025370, A343971, A344797.

{n: A025428(n) >= 4}. Union of A025370 and A025360. - R. J. Mathar, Jun 15 2018

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A343968 Numbers that are the sum of three positive cubes in four or more ways.

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A025407 Numbers that are the sum of 4 positive cubes in 3 or more ways.

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

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A344034 Numbers that are the sum of five positive cubes in four 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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A344352 Numbers that are the sum of four fourth powers in four or more ways.

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A025369 Numbers that are the sum of 4 nonzero squares in 4 or more ways.

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