A342688 Numbers that are the sum of five positive fifth powers in exactly three ways.

13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925

Offset: 1

Author

David Consiglio, Jr., May 18 2021

Keywords

• nonn

Comments

Differs from A342687:

287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5

= 9^5 + 13^5 + 26^5 + 37^5 + 46^5

= 11^5 + 12^5 + 23^5 + 41^5 + 44^5

= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.

So 287618651 is a term of A342687 but not a term of this sequence.

[Corrected by Patrick De Geest, Dec 28 2024]

Examples

			50043937 =  6^5 + 16^5 + 18^5 + 24^5 + 33^5
         =  7^5 + 13^5 + 21^5 + 23^5 + 33^5
         = 11^5 + 13^5 + 13^5 + 29^5 + 31^5
so 50043937 is a term of this sequence.
[Corrected by _Patrick De Geest_, Dec 28 2024]
		

Links

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

Crossrefs

Cf. A003350, A004845, A342685, A342686, A342687, A344244, A344519, A344518, A345863, A345864, A346257, A346358.

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 == 3])
for x in range(len(rets)):
    print(rets[x])