A346257 Numbers that are the sum of five fifth powers in exactly five ways.

9006349824, 65799210368, 67629776576, 181085909632, 188189635424, 295677350451, 467139768468, 471359089024, 656243139157, 691381929281, 797466940832, 854533526901, 874953049024, 891862586132, 953769598750, 1038549256768, 1092458681568, 1182658308657

Offset: 1

Author

David Consiglio, Jr., Jul 11 2021

Keywords

• nonn

Comments

Differs from 103 terms known at term 6 because 288203194368 = 48^5 + 84^5 + 96^5 + 108^5 + 192^5 = 16^5 + 99^5 + 103^5 + 121^5 + 189^5 = 42^5 + 68^5 + 86^5 + 148^5 + 184^5 = 16^5 + 68^5 + 124^5 + 136^5 + 184^5 = 16^5 + 82^5 + 94^5 + 158^5 + 178^5 = 24^5 + 36^5 + 144^5 + 156^5 + 168^5.

Examples

			9006349824 is a term because 9006349824 = 24^5 + 42^5 + 48^5 + 54^5 + 96^5 = 21^5 + 34^5 + 43^5 + 74^5 + 92^5 = 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.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..253

Crossrefs

Cf. A344359, A344519, A345863, A346360.

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, 1000)]
for pos in cwr(power_terms, 5):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 5])
    for x in range(len(rets)):
        print(rets[x])