A345843 Numbers that are the sum of nine fourth powers in exactly one ways.

9, 24, 39, 54, 69, 84, 89, 99, 104, 114, 119, 129, 134, 144, 149, 164, 169, 179, 184, 194, 199, 209, 214, 229, 244, 249, 259, 274, 329, 354, 369, 384, 409, 419, 434, 449, 484, 489, 499, 514, 569, 594, 609, 624, 633, 648, 649, 659, 663, 674, 678, 689, 693, 708

Offset

1,1

Comments

Differs from A003343 at term 28 because 264 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

24 is a term because 24 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 1])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A003343, A345793, A345833, A345844, A345853, A346336.

Sequence in context: A124065 A121453 A003343 * A047720 A320599 A293846

Adjacent sequences: A345840 A345841 A345842 * A345844 A345845 A345846

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved