

A242183


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.


12



6, 9, 15, 35, 36, 42, 48, 57, 63, 71, 72, 72, 75, 78, 90, 98, 100, 100, 120, 135, 141, 147, 147, 162, 195, 196, 204, 208, 215, 225, 225, 225, 243, 252, 260, 279, 280, 288, 289, 295, 300, 306, 336, 363, 364, 384, 405, 441, 450, 456, 456, 462, 504, 510, 525, 537
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

A242192(k) gives number of occurrences of k.  Reinhard Zumkeller, May 07 2014
See A300564 for the list of values without duplicates.  M. F. Hasler, Apr 16 2018


LINKS

Lars Blomberg, Table of n, a(n) for n = 1..2241


FORMULA

c = sqrt(sqrt(a^2+b^3)) is an integer.


EXAMPLE

6 is in the sequence because 6^4 = 28^2 + 8^3.
72 is in the sequence twice because 72^4 = 1728^2 + 288^3 = 4941^2 + 135^3.


MATHEMATICA

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 *)


PROG

(Haskell)
a242183 n = a242183_list !! (n1)
a242183_list = concatMap (\(r, x) > take r [x, x..]) $
zip a242192_list [1..]
 Reinhard Zumkeller, May 07 2014


CROSSREFS

Cf. A242184, A242185, A242186.
Sequence in context: A023885 A031209 A271826 * A300564 A316050 A272264
Adjacent sequences: A242180 A242181 A242182 * A242184 A242185 A242186


KEYWORD

nonn


AUTHOR

Lars Blomberg, May 06 2014


STATUS

approved



