A345623 Numbers that are the sum of nine fifth powers in six or more ways.

926404, 936607, 952896, 985421, 993574, 993605, 993816, 1075779, 1123321, 1133344, 1134367, 1151406, 1160105, 1166111, 1177144, 1206514, 1209669, 1209847, 1215545, 1225630, 1251130, 1264929, 1265320, 1278611, 1414834, 1422367, 1422609, 1430384, 1431367

Offset

1,1

Links

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

Example

936607 is a term because 936607 = 1^5 + 1^5 + 2^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 12^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5 = 1^5 + 3^5 + 5^5 + 6^5 + 8^5 + 8^5 + 11^5 + 11^5 + 14^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 9^5 + 11^5 + 11^5 + 14^5 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 8^5 + 10^5 + 12^5 + 14^5 = 4^5 + 4^5 + 4^5 + 7^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5.

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, 9):
    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])

Crossrefs

Cf. A345590, A345614, A345622, A345624, A345638, A346341.

Sequence in context: A105011 A345613 A346330 * A346341 A115172 A186557

Adjacent sequences: A345620 A345621 A345622 * A345624 A345625 A345626

Keyword

nonn

Author

David Consiglio, Jr., Jun 20 2021

Status

approved