A344921 Numbers that are the sum of four fourth powers in exactly six ways.

3847554, 5624739, 6044418, 6593538, 6899603, 9851058, 10456338, 11645394, 12378018, 13638738, 16990803, 19081089, 20622338, 20649603, 20755218, 20795763, 24174003, 24368769, 25265553, 25850178, 25899058, 28470339, 29195154, 30295539, 30534018, 30623394

Offset: 1

Author

David Consiglio, Jr., Jun 02 2021

Keywords

• nonn

Comments

Differs from A344904 at term 4 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.

Examples

			3847554 is a term 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.
		

Links

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

Crossrefs

Cf. A344357, A344648, A344904, A344923, A344941, A345149.

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 == 6])
for x in range(len(rets)):
    print(rets[x])