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%I #18 Apr 16 2018 11:38:44
%S 6,9,15,35,36,42,48,57,63,71,72,72,75,78,90,98,100,100,120,135,141,
%T 147,147,162,195,196,204,208,215,225,225,225,243,252,260,279,280,288,
%U 289,295,300,306,336,363,364,384,405,441,450,456,456,462,504,510,525,537
%N Integers c, listed with multiplicity, such that there is a solution to the equation a^2 + b^3 = c^4, with integers a, b > 0.
%C A242192(k) gives number of occurrences of k. - _Reinhard Zumkeller_, May 07 2014
%C See A300564 for the list of values without duplicates. - _M. F. Hasler_, Apr 16 2018
%H Lars Blomberg, <a href="/A242183/b242183.txt">Table of n, a(n) for n = 1..2241</a>
%F c = sqrt(sqrt(a^2+b^3)) is an integer.
%e 6 is in the sequence because 6^4 = 28^2 + 8^3.
%e 72 is in the sequence twice because 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.
%t f[n_] := f[n] = Module[{a}, Array[(a = Sqrt[n^4 - #^3]; If[ IntegerQ@ a && a > 0, {a, #}, Sequence @@ {}]) &, Floor[n^(4/3)]]];; k = 1; lst = {}; While[k < 3001, If[ f[k] != {}, AppendTo[lst, k]; Print[{k, f[k]}]]; k++]; s = Select[ Range[3000], f@# != {} &]; l = Length@ f@ # & /@ s; Flatten[ Table[ s[[#]], {l[[#]]}] & /@ Range@ Length@ s] (* _Robert G. Wilson v_, May 06 2014 *)
%o (Haskell)
%o a242183 n = a242183_list !! (n-1)
%o a242183_list = concatMap (\(r,x) -> take r [x,x..]) $
%o zip a242192_list [1..]
%o -- _Reinhard Zumkeller_, May 07 2014
%Y Cf. A242184, A242185, A242186.
%K nonn
%O 1,1
%A _Lars Blomberg_, May 06 2014
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