A346365 Numbers that are the sum of six fifth powers in exactly ten ways.

55302546200, 89999127392, 96110537743, 104484239200, 120492759200, 121258798144, 127794946400, 133364991375, 135030535200, 136156575744, 151305014432, 155434423925, 174388570400, 177099008000, 179272687000, 182844944832, 184948721056, 187873845500

Offset: 1

Author

David Consiglio, Jr., Jul 18 2021

Keywords

• nonn

Comments

This sequence differs from A344196:

180336745600 = 48^5 + 54^5 + 66^5 + 66^5 + 112^5 + 174^5

= 9^5 + 21^5 + 93^5 + 112^5 + 117^5 + 168^5

= 11^5 + 44^5 + 73^5 + 92^5 + 133^5 + 167^5

= 15^5 + 81^5 + 94^5 + 95^5 + 129^5 + 166^5

= 1^5 + 49^5 + 62^5 + 107^5 + 138^5 + 163^5

= 35^5 + 69^5 + 75^5 + 98^5 + 141^5 + 162^5

= 18^5 + 81^5 + 105^5 + 112^5 + 135^5 + 159^5

= 14^5 + 50^5 + 62^5 + 86^5 + 150^5 + 158^5

= 2^5 + 52^5 + 54^5 + 108^5 + 146^5 + 158^5

= 14^5 + 22^5 + 66^5 + 118^5 + 142^5 + 158^5

= 4^5 + 50^5 + 58^5 + 102^5 + 150^5 + 156^5,

so 180336745600 is in A344196, but is not in this sequence.

Examples

			55302546200 = 34^5 + 38^5 + 50^5 + 57^5 + 95^5 + 136^5
            = 23^5 + 49^5 + 61^5 + 69^5 + 107^5 + 131^5
            = 24^5 + 37^5 + 63^5 + 81^5 + 104^5 + 131^5
            = 21^5 + 35^5 + 60^5 + 94^5 + 100^5 + 130^5
            = 57^5 + 60^5 + 71^5 + 75^5 + 109^5 + 128^5
            = 19^5 + 37^5 + 56^5 + 96^5 + 104^5 + 128^5
            = 35^5 + 41^5 + 53^5 + 69^5 + 115^5 + 127^5
            = 16^5 + 49^5 + 53^5 + 83^5 + 112^5 + 127^5
            = 35^5 + 37^5 + 40^5 + 88^5 + 119^5 + 121^5
            = 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5
so 55302546200 is a term.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..57

Crossrefs

Cf. A344196, A345822, A346259, A346364.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 10])
    for x in range(len(rets)):
        print(rets[x])