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

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

1,1

Links

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

Example

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.

Prog

(Python)
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])

Crossrefs

Cf. A345603, A345627, A345641, A346355.

Sequence in context: A345625 A346343 A346342 * A346355 A339477 A234657

Adjacent sequences: A345639 A345640 A345641 * A345643 A345644 A345645

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved