A344737 Numbers that are the sum of three fourth powers in eight or more ways.

5745705602, 8185089458, 11054952818, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 37314202562, 38214512882, 41923075922, 46543615202, 49511121842, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63429959138

Offset: 1

Author

David Consiglio, Jr., May 27 2021

Keywords

• nonn

Examples

			5745705602 is a term because 5745705602 = 3^4 + 230^4 + 233^4 = 25^4 + 218^4 + 243^4 = 43^4 + 207^4 + 250^4 = 58^4 + 197^4 + 255^4 = 85^4 + 177^4 + 262^4 = 90^4 + 173^4 + 263^4 = 102^4 + 163^4 + 265^4 = 122^4 + 145^4 + 267^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..100

Crossrefs

Cf. A344729, A344738, A344750, A344924, A345087.

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, 3):
    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])