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A228946 Numbers m such that m^3 - k^3 is a square for some k < m, k > 0.

%I A228946 #33 Mar 20 2025 03:29:01
%S A228946 8,10,14,28,32,33,40,56,57,65,71,72,74,78,90,105,112,114,126,128,130,
%T A228946 132,140,148,154,155,160,176,193,200,217,218,224,228,250,252,260,266,
%U A228946 273,280,284,288,296,297,305,312,329,336,344,349,350,360,392
%N A228946 Numbers m such that m^3 - k^3 is a square for some k < m, k > 0.
%C A228946 See A038596 = A038597^2 for the possible values of n^3-k^3.
%H A228946 Nathaniel Johnston, <a href="/A228946/b228946.txt">Table of n, a(n) for n = 1..5000</a>
%F A228946 a(n) = A066648(n)^(1/3). - _Amiram Eldar_, Mar 20 2025
%p A228946 isA228946 := proc (n) local k; for k to n-1 do if issqr(n^3-k^3) then return true end if end do; return false end proc; for n from 1 to 400 do if isA228946(n)then print(n): end if: end do: # _Nathaniel Johnston_, Oct 07 2013
%t A228946 k3sQ[n_]:=Count[n^3-Range[n-1]^3,_?(IntegerQ[Sqrt[#]]&)]>0; Select[ Range[ 400],k3sQ] (* _Harvey P. Dale_, May 07 2017 *)
%o A228946 (PARI) for(n=1,999,for(k=1,n-1, issquare(n^3-k^3) & !print1(n",") & break))
%o A228946 (PARI) is(n)=for(k=1,n-1, issquare(n^3-k^3) & return(1))
%Y A228946 Cf. A001922, A038593-A038598, A014439, A014440, A014441, A066648, A071954.
%K A228946 nonn
%O A228946 1,1
%A A228946 _M. F. Hasler_, Oct 05 2013