A345820 - OEIS

A345820

Numbers that are the sum of six fourth powers in exactly eight ways.

58035, 59780, 87746, 96195, 96450, 102371, 106451, 106515, 108035, 108275, 108290, 108771, 112370, 112931, 115251, 122835, 122850, 124691, 125971, 133395, 133571, 133586, 134675, 136931, 138275, 138595, 143650, 144755, 145826, 147491, 148820, 149571, 150115

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OFFSET

1,1

COMMENTS

Differs from A345565 at term 4 because 88595 = 1^4 + 4^4 + 5^4 + 12^4 + 13^4 + 14^4 = 1^4 + 6^4 + 6^4 + 11^4 + 12^4 + 15^4 = 1^4 + 7^4 + 8^4 + 9^4 + 10^4 + 16^4 = 2^4 + 8^4 + 9^4 + 9^4 + 12^4 + 15^4 = 2^4 + 10^4 + 11^4 + 11^4 + 12^4 + 13^4 = 4^4 + 6^4 + 6^4 + 9^4 + 13^4 + 15^4 = 5^4 + 6^4 + 7^4 + 8^4 + 11^4 + 16^4 = 7^4 + 7^4 + 10^4 + 11^4 + 12^4 + 14^4.

LINKS

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

EXAMPLE

59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.

PROG

(Python)

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, 6):

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])