A344352 -id:A344352 - 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])

A344241 Numbers that are the sum of four fourth powers in three or more ways.

Original entry on oeis.org

16578, 43234, 49329, 53218, 54978, 57154, 93393, 106354, 107649, 108754, 138258, 151219, 160434, 168963, 173539, 177699, 178738, 181138, 183603, 185298, 195378, 195859, 196418, 197154, 197778, 201683, 202419, 209763, 211249, 216594, 217138, 223074, 234274, 235554, 235569, 236674, 237249, 237699

Offset: 1

David Consiglio, Jr., May 12 2021

nonn

			49329 = 2^4 + 2^4 + 12^4 + 13^4
      = 4^4 + 8^4 +  9^4 + 14^4
      = 6^4 + 9^4 + 12^4 + 12^4
so 49329 is a term of this sequence.

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

Cf. A025407, A309763, A344239, A344242, A344243, A344352, A345337.

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 >= 3])
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])

A344354 Numbers that are the sum of five fourth powers in four or more ways.

Original entry on oeis.org

20995, 21235, 31250, 41474, 43235, 43250, 43315, 43490, 43859, 45139, 46290, 47570, 51939, 53234, 53299, 54994, 56274, 57379, 57410, 57779, 59329, 59779, 63970, 67010, 67859, 68035, 68290, 71795, 71954, 73730, 73954, 75714, 75794, 77890, 82099, 84499, 86275, 86450, 87730, 92500, 93394, 93474, 93859

Offset: 1

David Consiglio, Jr., May 15 2021

nonn

			31250 is a term of this sequence because 31250 = 2^4 + 2^4 + 4^4 + 7^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 13^4 = 4^4 + 6^4 + 7^4 + 9^4 + 12^4 = 5^4 + 5^4 + 10^4 + 10^4 + 10^4.

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

Cf. A344034, A344243, A344352, A344355, A344358, A344518, A345561.

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, 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])

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

David Consiglio, Jr., May 15 2021

nonn

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

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])

A344277 Numbers that are the sum of three fourth powers in four or more ways.

Original entry on oeis.org

5978882, 15916082, 20621042, 22673378, 30623138, 33998258, 39765362, 48432482, 53809938, 61627202, 65413922, 74346818, 84942578, 88258898, 95662112, 103363442, 117259298, 128929682, 131641538, 137149922, 143244738, 155831858, 158811842, 167042642, 174135122, 175706258, 188529362

Offset: 1

David Consiglio, Jr., May 13 2021

nonn

			20621042 is a member of this sequence because 20621042 = 5^4 + 54^4 + 59^4 = 10^4 + 51^4 + 61^4 = 25^4 + 46^4 + 63^4 = 26^4 + 39^4 + 65^4

David Consiglio, Jr., Table of n, a(n) for n = 1..9084

Cf. A343968, A344239, A344278, A344352, A344364.

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,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])

cp's OEIS Frontend

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

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A344241 Numbers that are the sum of four fourth powers in three or more ways.

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

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A344354 Numbers that are the sum of five fourth powers in four or more ways.

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

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Python

A344277 Numbers that are the sum of three fourth powers in four or more ways.

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