A346343 - OEIS

A346343

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

1431398, 1431640, 1531397, 1952415, 2247917, 2530399, 2652563, 2652860, 2736790, 2851254, 2965588, 3088909, 3148674, 3273590, 3297416, 3329120, 3329362, 3332244, 3336895, 3345442, 3345653, 3361614, 3362217, 3364738, 3553641, 3571549, 3577951, 3609926, 3610155

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OFFSET

1,1

COMMENTS

Differs from A345625 at term 5 because 1969221 = 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 12^5 + 12^5 + 13^5 + 16^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 12^5 + 12^5 + 13^5 + 16^5 = 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 + 15^5 = 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 + 15^5 = 1^5 + 4^5 + 5^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 + 15^5 = 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 + 14^5 = 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 + 14^5.

LINKS

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

EXAMPLE

1431398 is a term because 1431398 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.

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 == 8])

for x in range(len(rets)):

print(rets[x])