A344187 Numbers that are the sum of two positive fourth powers in exactly one way.

2, 17, 32, 82, 97, 162, 257, 272, 337, 512, 626, 641, 706, 881, 1250, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2592, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 4802, 5392, 6497, 6562, 6577, 6642, 6817, 7186, 7857, 8192, 8962, 10001, 10016, 10081, 10256, 10625, 10657, 11296, 12401, 13122, 14096, 14642

Offset: 1

Author

David Consiglio, Jr., May 11 2021

Keywords

• nonn

Comments

Differs from A003336 at term 11660 because 635318657 = 59^4 + 158^4 = 133^4 + 134^4

Examples

			32 is a member of this sequence because 32 = 2^4 + 2^4
		

Links

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

Crossrefs

Cf. A003336, A338667, A344188.

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,2):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])