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URL: https://oeis.org/A003341

⇱ A003341 - OEIS

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A003341
Numbers that are the sum of 7 positive 4th powers.
40
7, 22, 37, 52, 67, 82, 87, 97, 102, 112, 117, 132, 147, 162, 167, 177, 182, 197, 212, 227, 242, 247, 262, 277, 292, 307, 322, 327, 337, 342, 352, 357, 372, 387, 402, 407, 417, 422, 437, 452, 467, 482, 487, 502, 517, 532, 547, 562, 567, 577, 582, 592, 597, 612, 627
OFFSET
1,1
REFERENCES
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 310.
LINKS
Eric Weisstein's World of Mathematics, Biquadratic Number.
EXAMPLE
From David A. Corneth, Aug 04 2020: (Start)
5971 is in the sequence as 5971 = 3^4 + 3^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4.
12022 is in the sequence as 12022 = 1^4 + 2^4 + 7^4 + 7^4 + 7^4 + 7^4 + 7^4.
16902 is in the sequence as 16902 = 1^4 + 1^4 + 3^4 + 6^4 + 7^4 + 9^4 + 9^4. (End)
MAPLE
N:= 1000:
S1:= {seq(i^4, i=1..floor(N^(1/4)))}:
S2:= select(`<=`, {seq(seq(i+j, i=S1), j=S1)}, N):
S4:= select(`<=`, {seq(seq(i+j, i=S2), j=S2)}, N):
S6:= select(`<=`, {seq(seq(i+j, i=S2), j=S4)}, N):
sort(convert(select(`<=`, {seq(seq(i+j, i=S1), j=S6)}, N), list)); # Robert Israel, Jul 21 2019
PROG
(Python)
from itertools import combinations_with_replacement as mc
def aupto(limit):
qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 6 <= limit]
ss = set(sum(c) for c in mc(qd, 7))
return sorted(s for s in ss if s <= limit)
print(aupto(630)) # Michael S. Branicky, Jul 22 2021
KEYWORD
nonn,easy
STATUS
approved