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

1,1

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.

Links

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

Example

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.

Prog

(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])

Crossrefs

Cf. A344196, A345822, A346259, A346364.

Sequence in context: A233553 A273928 A344196 * A295042 A320880 A015401

Adjacent sequences: A346362 A346363 A346364 * A346366 A346367 A346368

Keyword

nonn

Author

David Consiglio, Jr., Jul 18 2021

Status

approved