A344357 Numbers that are the sum of four fourth powers in exactly five ways.

2147874, 2266338, 2690658, 3189603, 3464178, 3754674, 4030419, 4165794, 4457298, 4884114, 5229378, 5978883, 5980178, 5981283, 6014178, 6134994, 6258723, 6313953, 6400194, 6612354, 7088898, 7498323, 7811874, 7918498, 8064018, 8292323, 8630259, 9146034, 9269523, 9388978, 9397683, 9726978

Offset: 1

Author

David Consiglio, Jr., May 15 2021

Keywords

• nonn

Comments

Differs from A344356 at term 7 because 3847554 = 2^4 + 13^4 + 29^4 + 42^4 = 2^4 + 21^4 + 22^4 + 43^4 = 6^4 + 11^4 + 17^4 + 44^4 = 6^4 + 31^4 + 32^4 + 37^4 = 9^4 + 29^4 + 32^4 + 38^4 = 13^4 + 26^4 + 32^4 + 39^4.

Examples

			2690658 is a term of this sequence because 2690658 = 2^4 + 8^4 + 33^4 + 35^4 = 3^4 + 4^4 + 19^4 + 40^4 = 7^4 + 8^4 + 30^4 + 37^4 = 9^4 + 21^4 + 30^4 + 36^4 = 16^4 + 25^4 + 32^4 + 33^4.
		

Links

• David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A343986, A344353, A344356, A344359, A344365, A344921.

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, 50)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 5])
for x in range(len(rets)):
    print(rets[x])