A344807 -id:A344807 - cp's OEIS frontend

A345512 Numbers that are the sum of six cubes in three or more ways.

221, 254, 369, 411, 443, 469, 495, 502, 576, 595, 600, 626, 648, 658, 684, 704, 711, 720, 739, 746, 753, 760, 765, 767, 772, 774, 779, 786, 793, 811, 818, 828, 830, 835, 837, 844, 854, 856, 863, 866, 873, 874, 880, 884, 886, 891, 892, 893, 899, 905, 910, 919

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			254 is a term because 254 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A048931, A343704, A344807, A345511, A345513, A345521, A345560.

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, 6):
    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])

A344796 Numbers that are the sum of five squares in three or more ways.

Original entry on oeis.org

29, 32, 35, 37, 40, 43, 44, 46, 51, 52, 53, 56, 58, 59, 61, 62, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112

Offset: 1

Sean A. Irvine, May 28 2021

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..20000

Cf. A025368, A294737, A343704, A344795, A344797, A344807.

A344806 Numbers that are the sum of six squares in two or more ways.

Original entry on oeis.org

21, 24, 29, 30, 33, 36, 38, 39, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			24 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2
   = 2^2 + 2^2 + 2^2 + 2^2 + 2^2 + 2^2
so 24 is a term.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A344795, A344805, A344807, A345479, A345511.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

A344808 Numbers that are the sum of six squares in four or more ways.

Original entry on oeis.org

36, 41, 44, 45, 53, 54, 56, 57, 60, 62, 63, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			41 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 6^2
   = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 5^2
   = 1^2 + 2^2 + 3^2 + 3^2 + 3^2 + 3^2
   = 2^2 + 2^2 + 2^2 + 2^2 + 3^2 + 4^2
so 41 is a term.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A344797, A344807, A344809, A345481, A345513.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 6):
    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])

A345480 Numbers that are the sum of seven squares in three or more ways.

Original entry on oeis.org

31, 34, 37, 39, 40, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			34 is a term because 34 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A344807, A345479, A345481, A345490, A345521.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    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])

cp's OEIS Frontend

A345512 Numbers that are the sum of six cubes in three or more ways.

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A344796 Numbers that are the sum of five squares in three or more ways.

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A344806 Numbers that are the sum of six squares in two or more ways.

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A344808 Numbers that are the sum of six squares in four or more ways.

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A345480 Numbers that are the sum of seven squares in three or more ways.

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Python