OFFSET
1,1
COMMENTS
This sequence differs from A345722:
9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
= 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
= 8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
= 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
= 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
= 8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
= 5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
= 8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
= 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
so 9085584992 is in A345722, but is not in this sequence.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..4934
EXAMPLE
2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5
= 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5
= 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5
= 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5
= 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5
= 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5
= 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5
= 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5,
so 2295937600 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 == 8])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
David Consiglio, Jr., Jul 13 2021
STATUS
approved