A003344 Numbers that are the sum of 10 positive 4th powers.

10, 25, 40, 55, 70, 85, 90, 100, 105, 115, 120, 130, 135, 145, 150, 160, 165, 170, 180, 185, 195, 200, 210, 215, 225, 230, 245, 250, 260, 265, 275, 280, 290, 295, 310, 325, 330, 340, 345, 355, 360, 370, 375, 385, 390, 400, 405, 410, 420, 425, 435, 440, 450, 455, 465

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Eric Weisstein's World of Mathematics, Biquadratic Number.

Example

From David A. Corneth, Aug 03 2020: (Start)
5176 is in the sequence as 5176 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 5^4 + 5^4 + 5^4 + 5^4 + 7^4.
6901 is in the sequence as 6901 = 1^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4 + 6^4 + 6^4.
8502 is in the sequence as 8502 = 1^4 + 3^4 + 4^4 + 5^4 + 5^4 + 5^4 + 6^4 + 6^4 + 6^4 + 7^4. (End)

Prog

(Python)
from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(limit):
    pows4 = list(takewhile(lambda x: x <= limit, (i**4 for i in count(1))))
    sum10 = set(sum(c) for c in mc(pows4, 10) if sum(c) <= limit)
    return sorted(sum10)
print(aupto(465)) # Michael S. Branicky, Oct 25 2021

Crossrefs

Cf. A000583, A003333, A003343, A003355, A047721, A345595, A345853.

Sequence in context: A003001 A198377 A038350 * A345853 A047721 A155576

Adjacent sequences: A003341 A003342 A003343 * A003345 A003346 A003347

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved