A342686 Numbers that are the sum of five fifth powers in exactly two ways.

4097, 51446, 51477, 51688, 52469, 54570, 59221, 68252, 68905, 84213, 110494, 131104, 151445, 212496, 300277, 325174, 325713, 355114, 422135, 422738, 589269, 637418, 794434, 810820, 876734, 876765, 876976, 877757, 879858, 884509, 893540, 909501, 924912, 935782, 976733, 995571, 1037784, 1083457

Offset: 1

Author

David Consiglio, Jr., May 18 2021

Keywords

• nonn

Comments

This sequence differs from A342685:

13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5

= 2^5 + 5^5 + 12^5 + 23^5 + 23^5

= 16^5 + 19^5 + 20^5 + 20^5 + 20^5,

so 13124675 is in A342685, but is not in this sequence.

Examples

			51477 = 2^5 + 4^5 + 7^5 + 7^5 + 7^5
      = 2^5 + 5^5 + 6^5 + 6^5 + 8^5
so 51477 is a term of this sequence.
		

Links

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

Crossrefs

Cf. A342685, A342688, A344237, A344643, A344645, A346357.

Programs

Python

from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 500)]
for pos in cwr(power_terms, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 2])
for x in range(len(rets)):
    print(rets[x])