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%I #21 Jan 24 2022 19:03:38
%S 82,626,706,2402,2482,3026,6562,6642,7186,8962,14642,14722,15266,
%T 17042,21202,28562,28642,29186,30962,35122,43202,50626,50706,51250,
%U 53026,57186,65266,79186,83522,83602,84146,85922,90082,98162,112082,130322,130402,130946,132722
%N Sums of two distinct odd fourth powers.
%e 82 is in the sequence since 82 = 1^4 + 3^4.
%e 626 is in the sequence since 626 = 1^4 + 5^4.
%t Quiet@Select[Range@60000,!Equal@@(a=First@PowersRepresentations[#,2,4])&&And@@OddQ@a&] (* _Giorgos Kalogeropoulos_, Apr 24 2021 *)
%t Union[Total/@Subsets[Range[1,19,2]^4,{2}]] (* _Harvey P. Dale_, Jan 24 2022 *)
%o (Python)
%o def aupto(limit):
%o ofps = [i**4 for i in range(1, int(limit**.25)+2, 2) if i**4 < limit]
%o ss = set(f+g for i, f in enumerate(ofps) for g in ofps[i+1:])
%o return sorted(s for s in ss if s <= limit)
%o print(aupto(132722)) # _Michael S. Branicky_, Apr 24 2021
%Y Cf. A339992 (sums of two distinct odd cubes), A343588.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, Apr 20 2021
%E More terms from _Jon E. Schoenfield_, Apr 20 2021
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