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%I #24 Jul 26 2021 15:46:40
%S 2,9,17,24,28,43,65,80,82,89,108,126,141,145,206,217,232,257,264,283,
%T 297,320,344,359,381,424,472,513,528,593,599,626,633,652,689,730,745,
%U 750,768,810,841,968,985,1001,1016,1081,1137,1256,1297,1304,1323,1332
%N Numbers of the form a^4 + b^3 with a, b > 0.
%H Vincenzo Librandi, <a href="/A100291/b100291.txt">Table of n, a(n) for n = 1..10000</a>
%H Gian Cordana Sanjaya and Xiaoheng Wang, <a href="https://arxiv.org/abs/2107.10380">On the squarefree values of a^4+b^3</a>, arXiv:2107.10380 [math.NT], 2021.
%t lst={}; Do[p=a^4+b^3; If[p<2000, AppendTo[lst, p]], {a, 64}, {b, 256}]; Union[lst]
%t With[{nn=20},Select[Union[#[[1]]^4+#[[2]]^3&/@Tuples[Range[20],2]],#<= nn^3+1&]] (* _Harvey P. Dale_, May 27 2020 *)
%o (PARI) is(n)=for(a=1, sqrtnint(n-1, 4), ispower(n-a^4, 3) && return(a)) \\ Returns a > 0 if n is in the sequence, or 0 otherwise. - _M. F. Hasler_, Apr 25 2018
%o (PARI) list(lim)=my(v=List());for(b=1,sqrtnint(lim\=1,3), my(b3=b^3); for(a=1,sqrtnint(lim-b3,4), listput(v,a^4+b3))); Set(v) \\ _Charles R Greathouse IV_, Jul 26 2021
%Y Cf. A100271 (primes of the form a^4 + b^3).
%Y Cf. A055394 (a^2 + b^3: contains this as subsequence), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4), A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).
%Y Roots of 5th powers are listed in A300565 (z^5 = x^3 + y^4); see also A300564 (z^4 = x^2 + y^3) and A242183, A300566 (z^6 = x^4 + y^5), A300567 (z^7 = x^6 + y^5), A302174.
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 18 2004
%E Edited by _M. F. Hasler_, Apr 25 2018
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