A344796 -id:A344796 - cp's OEIS frontend

A343704 Numbers that are the sum of five positive cubes in three or more ways.

766, 810, 827, 829, 865, 883, 981, 1018, 1025, 1044, 1070, 1105, 1108, 1142, 1145, 1161, 1168, 1226, 1233, 1252, 1259, 1289, 1350, 1368, 1376, 1424, 1431, 1439, 1441, 1457, 1461, 1487, 1492, 1494, 1522, 1529, 1531, 1538, 1548, 1550, 1555, 1568, 1583, 1585, 1587, 1590, 1592, 1593, 1594, 1609, 1611, 1613, 1639

Offset: 1

David Consiglio, Jr., Apr 26 2021

This sequence differs from A343705 at term 20 because 1252 = 1^3+1^3+5^3+5^3+10^3= 1^3+2^3+3^3+6^3+10^3 = 3^3+3^3+7^3+7^3+8^3 = 3^3+4^3+6^3+6^3+9^3. Thus this term is in this sequence but not A343705.

			827 is a member of this sequence because 827 = 1^3 + 4^3 + 5^3 + 5^3 + 8^3 = 2^3 + 2^3 + 5^3 + 7^3 + 7^3 = 2^3 + 3^3 + 4^3 + 6^3 + 8^3.

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

Cf. A025407, A343702, A343705, A344034, A344243, A344796, A345512.

Select[Range@2000,Length@Select[PowersRepresentations[#,5,3],FreeQ[#,0]&]>2&] (* Giorgos Kalogeropoulos, Apr 26 2021 *)

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)]#n
for pos in cwr(power_terms,5):#m
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v >= 3])#s
for x in range(len(rets)):
    print(rets[x])

A025368 Numbers that are the sum of 4 nonzero squares in 3 or more ways.

Original entry on oeis.org

28, 42, 52, 55, 58, 60, 63, 66, 67, 70, 73, 75, 76, 78, 79, 82, 84, 85, 87, 90, 91, 92, 93, 95, 97, 98, 99, 100, 102, 103, 105, 106, 108, 109, 110, 111, 112, 114, 115, 117, 118, 119, 121, 122, 123, 124, 125, 126, 127, 129, 130, 132, 133, 134, 135, 137, 138, 139, 140, 141

Offset: 1

David W. Wilson

nonn

Index entries for sequences related to sums of squares

Cf. A025331, A025359, A025367, A025369, A025407, A344796.

{n: A025428(n) >=3}. Union of A025369 and A025359.- R. J. Mathar, Jun 15 2018

A344795 Numbers that are the sum of five squares in two or more ways.

Original entry on oeis.org

20, 29, 32, 35, 37, 38, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 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

Sean A. Irvine, May 28 2021

nonn

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

Cf. A025367, A047700, A294736, A343702, A344796, A344806.

A344797 Numbers that are the sum of five squares in four or more ways.

Original entry on oeis.org

53, 56, 59, 61, 62, 64, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 82, 83, 84, 85, 86, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126

Offset: 1

Sean A. Irvine, May 28 2021

nonn

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

Cf. A025369, A294738, A344034, A344796, A344797, A344798, A344808.

A344807 Numbers that are the sum of six squares in three or more ways.

Original entry on oeis.org

30, 33, 36, 38, 39, 41, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 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, 102, 103

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			33 = 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2
   = 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2
   = 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2
so 33 is a term.

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

Cf. A344796, A344806, A344808, A345480, A345512.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

cp's OEIS Frontend

A343704 Numbers that are the sum of five positive cubes in three or more ways.

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A025368 Numbers that are the sum of 4 nonzero squares in 3 or more ways.

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A344795 Numbers that are the sum of five squares in two or more ways.

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A344797 Numbers that are the sum of five squares in four or more ways.

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A344807 Numbers that are the sum of six squares in three or more ways.

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