A345641 -id:A345641 - cp's OEIS frontend

A345602 Numbers that are the sum of ten fourth powers in nine or more ways.

6820, 6870, 6885, 6950, 7060, 7110, 7125, 7285, 7350, 7860, 7925, 7990, 8020, 8035, 8100, 8165, 8230, 8245, 8260, 8275, 8325, 8340, 8390, 8405, 8515, 8565, 8580, 8645, 8755, 8820, 8884, 8965, 8995, 9030, 9045, 9060, 9075, 9125, 9140, 9205, 9220, 9235, 9270

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			6870 is a term because 6870 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 4^4 + 9^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4 + 8^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 = 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 = 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4 + 7^4.

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

Cf. A345557, A345593, A345601, A345603, A345641, A345861.

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, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])

A345626 Numbers that are the sum of nine fifth powers in nine or more ways.

Original entry on oeis.org

1969221, 2596936, 3353186, 3378178, 3923426, 3981447, 4094027, 4096729, 4112329, 4114188, 4129465, 4137209, 4147736, 4157156, 4170112, 4172994, 4254304, 4303773, 4410482, 4475846, 4477936, 4483379, 4485480, 4492410, 4501441, 4510461, 4543232, 4652011, 4691855

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			2596936 is a term because 2596936 = 1^5 + 1^5 + 4^5 + 5^5 + 9^5 + 13^5 + 13^5 + 13^5 + 17^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 17^5 = 1^5 + 4^5 + 7^5 + 7^5 + 7^5 + 9^5 + 9^5 + 14^5 + 18^5 = 1^5 + 5^5 + 6^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 12^5 + 13^5 + 14^5 + 17^5 = 2^5 + 5^5 + 5^5 + 6^5 + 6^5 + 6^5 + 15^5 + 15^5 + 16^5 = 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 9^5 + 12^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 11^5 + 11^5 + 13^5 + 18^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 9^5 + 16^5 + 17^5.

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

Cf. A345593, A345617, A345625, A345627, A345641, A346344.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])

A345640 Numbers that are the sum of ten fifth powers in eight or more ways.

Original entry on oeis.org

944383, 953139, 953414, 985453, 1118585, 1151438, 1185375, 1192180, 1198879, 1206546, 1209912, 1216569, 1217172, 1218912, 1223321, 1225398, 1226654, 1234631, 1241834, 1242437, 1251195, 1251406, 1252123, 1259685, 1265563, 1265594, 1267937, 1275375, 1281736

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			953139 is a term because 953139 = 1^5 + 1^5 + 1^5 + 3^5 + 8^5 + 10^5 + 10^5 + 10^5 + 12^5 + 13^5 = 1^5 + 2^5 + 2^5 + 6^5 + 6^5 + 8^5 + 9^5 + 9^5 + 12^5 + 14^5 = 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 12^5 + 12^5 + 13^5 = 2^5 + 2^5 + 3^5 + 3^5 + 7^5 + 7^5 + 9^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 11^5 + 11^5 + 12^5 + 13^5 = 2^5 + 3^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5 = 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 6^5 + 10^5 + 10^5 + 13^5 + 13^5 = 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 + 15^5.

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

Cf. A345601, A345625, A345639, A345641, A346353.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 10):
    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])

A346354 Numbers that are the sum of ten fifth powers in exactly nine ways.

Original entry on oeis.org

1192180, 1226654, 1242437, 1431399, 1431430, 1431672, 1431883, 1432453, 1432664, 1434765, 1439174, 1441695, 1442718, 1447602, 1448447, 1455346, 1455377, 1464166, 1474431, 1474462, 1475485, 1491978, 1497619, 1531429, 1539173, 1614736, 1671199, 1671410, 1672937

Offset: 1

David Consiglio, Jr., Jul 13 2021

nonn

Differs from A345641 at term 6 because 1431641 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 1^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 1^5 + 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 1^5 + 1^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 3^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 3^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.

			1192180 is a term because 1192180 = 5^5 + 5^5 + 5^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 16^5 = 2^5 + 5^5 + 5^5 + 5^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 16^5 = 3^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 6^5 + 8^5 + 13^5 + 15^5 = 3^5 + 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 7^5 + 7^5 + 13^5 + 15^5 = 2^5 + 2^5 + 2^5 + 3^5 + 8^5 + 8^5 + 9^5 + 9^5 + 12^5 + 15^5 = 1^5 + 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 12^5 + 13^5 + 13^5 = 1^5 + 2^5 + 2^5 + 2^5 + 4^5 + 11^5 + 11^5 + 12^5 + 12^5 + 13^5 = 6^5 + 9^5 + 9^5 + 10^5 + 11^5 + 11^5 + 11^5 + 11^5 + 11^5 + 11^5.

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

Cf. A345641, A345861, A346344, A346353, A346355.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 9])
    for x in range(len(rets)):
        print(rets[x])

A345642 Numbers that are the sum of ten fifth powers in ten or more ways.

Original entry on oeis.org

1431641, 1439416, 1464377, 1464408, 1505660, 1531398, 1531640, 1564165, 1697929, 1703935, 1782171, 1969222, 1969253, 1969464, 1976997, 1985183, 1986028, 2000966, 2001989, 2028270, 2042460, 2052415, 2058421, 2059202, 2060522, 2069221, 2076393, 2130272, 2182162

Offset: 1

David Consiglio, Jr., Jun 20 2021

nonn

			1439416 is a term because 1439416 = 1^5 + 1^5 + 2^5 + 7^5 + 8^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 = 1^5 + 2^5 + 3^5 + 6^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 3^5 + 5^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 1^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 2^5 + 2^5 + 3^5 + 4^5 + 6^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 3^5 + 6^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 3^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 7^5 + 11^5 + 11^5 + 16^5 = 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5.

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

Cf. A345603, A345627, A345641, A346355.

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 10])
    for x in range(len(rets)):
        print(rets[x])

cp's OEIS Frontend

A345602 Numbers that are the sum of ten fourth powers in nine or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345626 Numbers that are the sum of nine fifth powers in nine or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A345640 Numbers that are the sum of ten fifth powers in eight or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python

A346354 Numbers that are the sum of ten fifth powers in exactly nine ways.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A345642 Numbers that are the sum of ten fifth powers in ten or more ways.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Python