A344922 Numbers that are the sum of four fourth powers in seven or more ways.

6576339, 13155858, 16020018, 16408434, 22673634, 23056803, 26421474, 33734834, 35965458, 39786098, 39803778, 43583138, 51071619, 52652754, 53731458, 57976083, 63985314, 64365939, 67655779, 68846274, 73744563, 75951138, 77495778, 87038883, 88648914, 89148114

Offset: 1

Author

David Consiglio, Jr., Jun 02 2021

Keywords

• nonn

Examples

			6576339 is a term because 6576339 = 1^4 + 24^4 + 41^4 + 43^4  = 3^4 + 7^4 + 41^4 + 44^4  = 4^4 + 23^4 + 27^4 + 49^4  = 6^4 + 31^4 + 41^4 + 41^4  = 7^4 + 11^4 + 36^4 + 47^4  = 7^4 + 21^4 + 28^4 + 49^4  = 12^4 + 17^4 + 29^4 + 49^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A344729, A344904, A344923, A344924, A344942, A345150.

Programs

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, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 7])
for x in range(len(rets)):
    print(rets[x])