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
KEYWORD
nonn
AUTHOR
David Consiglio, Jr., Jul 18 2021
STATUS
approved