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A342688
Numbers that are the sum of five fifth powers in exactly three ways.
6
13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925
OFFSET
1,1
COMMENTS
Differs from A342687:
287618651 = 9^5 + 22^5 + 28^5 + 28^5 + 49^5
= 10^5 + 14^5 + 27^5 + 38^5 + 47^5
= 12^5 + 13^5 + 24^5 + 42^5 + 45^5
= 12^5 + 21^5 + 23^5 + 31^5 + 49^5.
So 287618651 is a term of A342687 but not a term of this sequence.
LINKS
David Consiglio, Jr., Table of n, a(n) for n = 1..1000
EXAMPLE
50043937 = 7^5 + 17^5 + 19^5 + 25^5 + 34^5
= 8^5 + 14^5 + 22^5 + 24^5 + 34^5
= 12^5 + 14^5 + 14^5 + 30^5 + 32^5
so 50043937 is a term of this sequence.
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, 500)]
for pos in cwr(power_terms, 5):
tot = sum(pos)
keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 3])
for x in range(len(rets)):
print(rets[x])
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved