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A344833
a(n) is the number of ways to write n as Sum_{k = 2..14} x_k^k with x_k > 0 for k = 2..14.
1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 2, 1, 0, 1, 1, 2, 0, 3, 1, 0, 1, 0, 4, 0, 1, 2, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 1, 3, 1, 4, 0, 2, 3, 0, 1, 0, 4, 2, 2, 2, 1
OFFSET
1,28
COMMENTS
Liu and Zhao show that there is a finite number of zeros in the sequence.
LINKS
Jianya Liu and Lilu Zhao, Representation by sums of unlike powers, arXiv:2105.12955 [math.NT], 2021.
PROG
(PARI) See Links section.
(Python)
from collections import Counter
from itertools import count, takewhile, product
def aupto(lim):
pows = [None for k in range(15)]
for k in range(2, 15):
pows[k] = list(takewhile(lambda x: x<=lim-13, (i**k for i in count(1))))
cts = Counter(sum(p) for p in product(*(pows[k] for k in range(2, 15))))
return [cts[i] for i in range(1, lim+1)]
print(aupto(87)) # Michael S. Branicky, May 29 2021
CROSSREFS
Cf. A078359.
Sequence in context: A092573 A307801 A186717 * A233286 A305802 A375483
KEYWORD
nonn
AUTHOR
Rémy Sigrist, May 29 2021
STATUS
approved