A344729 Numbers that are the sum of three fourth powers in seven or more ways.

779888018, 5745705602, 8185089458, 11054952818, 12478208288, 14355295682, 21789116258, 22247419922, 26839201298, 29428835618, 31861462178, 33038379458, 37314202562, 38214512882, 41923075922, 46543615202, 49511121842, 51711350418, 54438780578, 56255300738, 59223741122, 62862779042, 63170929458, 63429959138, 71035097042, 71447292098, 73526154338, 73665805122, 81629817458

Offset: 1

Author

David Consiglio, Jr., May 27 2021

Keywords

• nonn

Examples

			779888018 is a term because 779888018 = 3^4+ 139^4+ 142^4 = 9^4+ 38^4+ 167^4 = 14^4+ 133^4+ 147^4 = 43^4+ 114^4+ 157^4 = 47^4+ 111^4+ 158^4 = 63^4+ 98^4+ 161^4 = 73^4+ 89^4+ 162^4
		

Links

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

Crossrefs

Cf. A344647, A344730, A344737, A344922, A345086.

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 >= 7])
for x in range(len(rets)):
    print(rets[x])