A344519 Numbers that are the sum of five positive fifth powers in exactly four ways.

287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9051501568, 9203796832, 9254212901

Offset: 1

Author

David Consiglio, Jr., May 21 2021

Keywords

• nonn

Comments

Differs from A344518 at term 20 because

9006349824 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5

= 8^5 + 41^5 + 47^5 + 79^5 + 89^5

= 12^5 + 18^5 + 72^5 + 78^5 + 84^5

= 21^5 + 34^5 + 43^5 + 74^5 + 92^5

= 24^5 + 42^5 + 48^5 + 54^5 + 96^5.

Examples

			287618651 is a term because
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.
[Corrected by _Patrick De Geest_, Dec 28 2024]
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..4857

Crossrefs

Cf. A003350, A004845, A342685, A342686, A342687, A342688, A344244, A344355, A344518, A345863, A345864, A346257, A346358, A346359.

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 == 4])
for x in range(len(rets)):
    print(rets[x])