A343972 -id:A343972 - cp's OEIS frontend

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

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

David Consiglio, Jr., May 05 2021

nonn

			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.

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

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

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])

A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

Original entry on oeis.org

13896, 40041, 44946, 52200, 53136, 58995, 76168, 82278, 93339, 94184, 105552, 110683, 111168, 112384, 112832, 113400, 143424, 149416, 149904, 167616, 169560, 171296, 175104, 196776, 197569, 208144, 216126, 221696, 222984, 224505, 235808, 240813, 252062, 255312, 262781, 266031, 281728, 291213

Offset: 1

David Consiglio, Jr., May 05 2021

nonn

Differs from A343968 at term 20 because 161568 = 2^3 + 16^3 + 54^3 = 9^3 + 15^3 + 54^3 = 17^3 + 39^3 + 46^3 = 18^3 + 19^3 + 53^3 = 26^3 + 36^3 + 46^3.

			44946 is a term because 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.

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

Cf. A025324, A025397, A343968, A343970, A343972, A344278, A345865.

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])

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

David Consiglio, Jr., May 06 2021

nonn

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.

			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.

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

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

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])

A344035 Numbers that are the sum of five positive cubes in exactly four ways.

Original entry on oeis.org

1252, 1376, 1461, 1522, 1548, 1585, 1590, 1646, 1702, 1709, 1737, 1739, 1772, 1798, 1802, 1810, 1864, 1889, 1954, 1987, 2006, 2033, 2081, 2096, 2152, 2160, 2225, 2241, 2251, 2276, 2313, 2322, 2339, 2341, 2367, 2374, 2377, 2416, 2423, 2456, 2458, 2465, 2467, 2512, 2521, 2528, 2530, 2537, 2540, 2549, 2556, 2582

Offset: 1

David Consiglio, Jr., May 07 2021

nonn

Differs from A344034 at term 13 because 1765 = 1^3 + 1^3 + 2^3 + 3^3 + 12^3 = 1^3 + 1^3 + 6^3 + 6^3 + 11^3 = 1^3 + 2^3 + 3^3 + 9^3 + 10^3 = 3^3 + 4^3 + 6^3 + 9^3 + 9^3 = 4^3 + 4^3 + 5^3 + 8^3 + 10^3

			1461 is a member of this sequence because 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

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

Cf. A294738, A343705, A343972, A343988, A344034, A344355, A345766.

s5pcQ[n_]:=Length[Select[PowersRepresentations[n,5,3],FreeQ[#,0]&]]==4; Select[Range[ 3000],s5pcQ] (* Harvey P. Dale, Sep 15 2024 *)

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])

A344353 Numbers that are the sum of four fourth powers in exactly four 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

Differs from A344352 at term 52 because 2147874 = 2^4 + 14^4 + 31^4 + 33^4 = 4^4 + 23^4 + 27^4 + 34^4 = 7^4 + 21^4 + 28^4 + 34^4 = 12^4 + 17^4 + 29^4 + 34^4 = 14^4 + 18^4 + 19^4 + 37^4.

			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. A343972, A344242, A344278, A344352, A344355, A344357.

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])

A025405 Numbers that are the sum of 4 positive cubes in exactly 3 ways.

Original entry on oeis.org

1225, 1521, 1582, 1584, 1738, 1764, 2009, 2249, 2366, 2415, 2422, 2457, 2459, 2485, 2520, 2539, 2753, 2763, 2790, 2799, 3008, 3094, 3185, 3187, 3213, 3248, 3276, 3392, 3456, 3458, 3465, 3572, 3582, 3600, 3607, 3626, 3656, 3717, 3736, 3753, 3815, 3941

Offset: 1

David W. Wilson

nonn

Cf. A025359, A025397, A025404, A025407, A343705, A343972, A344242.

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

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

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A343969 Numbers that are the sum of three positive cubes in exactly 4 ways.

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

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A344035 Numbers that are the sum of five positive cubes in exactly four ways.

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A344353 Numbers that are the sum of four fourth powers in exactly four ways.

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A025405 Numbers that are the sum of 4 positive cubes in exactly 3 ways.

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