A345150 -id:A345150 - cp's OEIS frontend

A345152 Numbers that are the sum of four third powers in eight or more ways.

21896, 27720, 30429, 31339, 31402, 33579, 34624, 34776, 36162, 36225, 40105, 42120, 42695, 44037, 44163, 44226, 44947, 45162, 45675, 46277, 46683, 46872, 46900, 47600, 48321, 48825, 49042, 50112, 50689, 50806, 50904, 51058, 51408, 51480, 51506, 51597, 51688

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

			30429 is a term because 30429 = 1^3 + 4^3 + 7^3 + 30^3  = 1^3 + 16^3 + 17^3 + 26^3  = 2^3 + 12^3 + 21^3 + 25^3  = 3^3 + 3^3 + 14^3 + 29^3  = 4^3 + 17^3 + 21^3 + 23^3  = 5^3 + 11^3 + 15^3 + 28^3  = 6^3 + 6^3 + 22^3 + 25^3  = 7^3 + 14^3 + 18^3 + 26^3.

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

Cf. A025373, A344924, A345087, A345146, A345150, A345153, A345183.

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 >= 8])
for x in range(len(rets)):
    print(rets[x])

A344922 Numbers that are the sum of four fourth powers in seven or more ways.

Original entry on oeis.org

6576339, 13155858, 16020018, 16408434, 22673634, 23056803, 26421474, 33734834, 35965458, 39786098, 39803778, 43583138, 51071619, 52652754, 53731458, 57976083, 63985314, 64365939, 67655779, 68846274, 73744563, 75951138, 77495778, 87038883, 88648914, 89148114

Offset: 1

David Consiglio, Jr., Jun 02 2021

nonn

			6576339 is a term because 6576339 = 1^4 + 24^4 + 41^4 + 43^4  = 3^4 + 7^4 + 41^4 + 44^4  = 4^4 + 23^4 + 27^4 + 49^4  = 6^4 + 31^4 + 41^4 + 41^4  = 7^4 + 11^4 + 36^4 + 47^4  = 7^4 + 21^4 + 28^4 + 49^4  = 12^4 + 17^4 + 29^4 + 49^4.

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Cf. A344729, A344904, A344923, A344924, A344942, A345150.

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, 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 == 7])
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

David Consiglio, Jr., Jun 09 2021

nonn

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

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])

A345180 Numbers that are the sum of five third powers in seven or more ways.

Original entry on oeis.org

4392, 4472, 4544, 4600, 4915, 4957, 5076, 5113, 5120, 5132, 5139, 5165, 5174, 5256, 5321, 5347, 5354, 5384, 5391, 5410, 5445, 5474, 5481, 5507, 5543, 5617, 5624, 5643, 5678, 5715, 5741, 5760, 5769, 5797, 5832, 5834, 5860, 5895, 5914, 5923, 5984, 5986, 6049

Offset: 1

David Consiglio, Jr., Jun 10 2021

nonn

			4472 is a term because 4472 = 1^3 + 4^3 + 4^3 + 4^3 + 15^3  = 2^3 + 2^3 + 9^3 + 11^3 + 11^3  = 2^3 + 3^3 + 4^3 + 5^3 + 15^3  = 2^3 + 3^3 + 7^3 + 11^3 + 12^3  = 3^3 + 3^3 + 6^3 + 10^3 + 13^3  = 3^3 + 4^3 + 5^3 + 8^3 + 14^3  = 5^3 + 5^3 + 7^3 + 10^3 + 12^3.

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

Cf. A344800, A344942, A345150, A345174, A345181, A345183, A345516.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 7])
for x in range(len(rets)):
    print(rets[x])

A025372 Numbers that are the sum of 4 nonzero squares in 7 or more ways.

Original entry on oeis.org

130, 135, 138, 148, 150, 154, 162, 170, 172, 175, 178, 180, 182, 183, 186, 187, 189, 190, 195, 196, 198, 199, 202, 207, 210, 213, 214, 215, 217, 218, 220, 222, 223, 225, 226, 228, 229, 230, 231, 234, 235, 237, 238, 242, 243, 244, 245, 246, 247, 250, 252, 253, 255, 258

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to sums of squares

Cf. A025335, A025363, A025371, A025373, A344800, A345150.

N:= 1000: # for terms <= N
B:= Vector(N):
for i from 1 while 4*i^2 <= N do
  for j from i while i^2 + 3*j^2 <= N do
    for k from j while i^2 + j^2 + 2*k^2 <= N do
      for l from k do
        m:= i^2 + j^2 + k^2 + l^2;
        if m > N then break fi;
        B[m]:= B[m]+1
od od od od:
select(t -> B[t] >= 7, [$1..N]); # Robert Israel, Oct 23 2020

{n: A025428(n) >= 7}. - R. J. Mathar, Jun 15 2018

A345086 Numbers that are the sum of three third powers in seven or more ways.

Original entry on oeis.org

2016496, 2562624, 4525632, 4783680, 5268024, 5618250, 6366816, 6525000, 6755328, 7374375, 7451352, 7457120, 8275392, 9063144, 9086104, 9931167, 10036872, 10266138, 10371024, 10973880, 12002472, 12452049, 12742920, 12983517, 13581352, 13639816, 13641480

Offset: 1

David Consiglio, Jr., Jun 07 2021

nonn

			2016496 is a term because 2016496 = 5^3 + 71^3 + 117^3 = 9^3 + 65^3 + 119^3 = 18^3 + 20^3 + 125^3 = 46^3 + 96^3 + 99^3 = 53^3 + 59^3 + 117^3 = 65^3 + 89^3 + 99^3 = 82^3 + 84^3 + 93^3.

David Consiglio, Jr., Table of n, a(n) for n = 1..100

Cf. A025335, A344729, A345083, A345085, A345087, A345150.

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, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 7])
for x in range(len(rets)):
    print(rets[x])

A345151 Numbers that are the sum of four third powers in exactly seven ways.

Original entry on oeis.org

13104, 18928, 19376, 20755, 21203, 22743, 24544, 24570, 24787, 25172, 25928, 27755, 27846, 28917, 29582, 31031, 31248, 31528, 32858, 34056, 34713, 35289, 35317, 35441, 35497, 35712, 36190, 36288, 36610, 36890, 36946, 38080, 39221, 39440, 39464, 39851, 39942

Offset: 1

David Consiglio, Jr., Jun 09 2021

nonn

Differs from A345150 at term 6 because 21896 = 1^3 + 11^3 + 19^3 + 22^3 = 2^3 + 2^3 + 12^3 + 26^3 = 2^3 + 3^3 + 19^3 + 23^3 = 2^3 + 5^3 + 15^3 + 25^3 = 3^3 + 10^3 + 16^3 + 24^3 = 3^3 + 17^3 + 19^3 + 19^3 = 4^3 + 6^3 + 20^3 + 22^3 = 5^3 + 8^3 + 14^3 + 25^3 = 7^3 + 11^3 + 17^3 + 23^3 = 8^3 + 9^3 + 19^3 + 22^3.

			13104 is a term 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.

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

Cf. A025363, A344923, A345085, A345149, A345150, A345153, A345181.

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 == 7])
for x in range(len(rets)):
    print(rets[x])

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A345152 Numbers that are the sum of four third powers in eight or more ways.

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A344922 Numbers that are the sum of four fourth powers in seven or more ways.

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

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Python

A345180 Numbers that are the sum of five third powers in seven or more ways.

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A025372 Numbers that are the sum of 4 nonzero squares in 7 or more ways.

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A345086 Numbers that are the sum of three third powers in seven or more ways.

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Python

A345151 Numbers that are the sum of four third powers in exactly seven ways.

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Python