BBC Russian

A345584

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

15427, 16692, 17348, 17493, 17972, 17987, 18052, 18227, 19267, 19412, 19492, 19507, 19572, 19747, 19748, 20116, 20787, 20852, 21268, 21283, 21333, 21348, 21413, 21443, 21493, 21508, 21523, 21588, 21637, 21652, 21653, 21827, 21877, 21892, 21957, 21972, 22037

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

16692 is a term because 16692 = 1^4 + 1^4 + 1^4 + 1^4 + 6^4 + 6^4 + 8^4 + 10^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 9^4 + 10^4 = 1^4 + 1^4 + 2^4 + 5^4 + 6^4 + 8^4 + 8^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 5^4 + 6^4 + 11^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 + 8^4 + 10^4 = 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 1^4 + 3^4 + 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 5^4 + 7^4 + 9^4 + 9^4 = 2^4 + 3^4 + 4^4 + 5^4 + 6^4 + 6^4 + 9^4 + 9^4.

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, 8):

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])