A345588 - OEIS

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A345588

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

2854, 2919, 2934, 2949, 2964, 3014, 3029, 3094, 3159, 3174, 3189, 3204, 3254, 3269, 3429, 3444, 3558, 3573, 3638, 3798, 3813, 3974, 4034, 4134, 4149, 4164, 4179, 4182, 4209, 4214, 4229, 4244, 4274, 4294, 4309, 4374, 4389, 4404, 4419, 4439, 4454, 4469, 4484

(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

2919 is a term because 2919 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.

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, 9):

tot = sum(pos)

keep[tot] += 1

rets = sorted([k for k, v in keep.items() if v >= 4])

for x in range(len(rets)):

print(rets[x])