OFFSET
1,1
COMMENTS
Corresponding fourth powers are 6561, 614656, 1500625, 8503056, 17850625, 26873856, 68574961, 252047376, 312900721, 322417936, 533794816, 1097199376, 1121513121, 1275989841, 1632240801, 2217373921, 2300257521, 2517630976, 3486784401, ...
2 is the first number that its 4th power, 2^4, is the sum of 2 positive cubes and is not the sum of 3 nonzero squares. 16 is the second number for this case. So 2 and 16 are not in this sequence.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
EXAMPLE
9 is a term because 9^4 = 9^3 + 18^3 = 1^2 + 28^2 + 76^2.
28 is a term because 28^4 = 28^3 + 84^3 = 64^2 + 144^2 + 768^2.
35 is a term because 35^4 = 70^3 + 105^3 = 1^2 + 600^2 + 1068^2.
54 is a term because 54^4 = 162^3 + 162^3 = 12^2 + 264^2 + 2904^2.
399 is a term because 399^4 = 665^3 + 2926^3 = 17^2 + 11236^2 + 158804^2.
PROG
(PARI) isA000408(n) = {my(a, b); a=1; while(a^2+1<n, b=1; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1)); b++; ); a++; ); return(0); }
T=thueinit('z^3+1);
isA003325(n)=#select(v->min(v[1], v[2])>0, thue(T, n))>0
for(n=3, 1e3, if(isA000408(n^4) && isA003325(n^4), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 19 2016
EXTENSIONS
Added missing term a(32), Chai Wah Wu, Jan 31 2016
STATUS
approved