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A038862 Numbers ending with '7' that are the difference of two positive cubes.

%I A038862 #14 Jan 12 2022 13:53:14
%S A038862 7,37,117,127,217,387,397,547,657,817,1027,1197,1267,1387,1647,1657,
%T A038862 1727,2107,2437,2457,2717,2977,3087,3367,3997,4167,4447,4697,4977,
%U A038862 5167,5677,5707,6327,6347,6487,6517,7057,7317,7657,7957,8587,8937,9197,9317
%N A038862 Numbers ending with '7' that are the difference of two positive cubes.
%H A038862 Robert Israel, <a href="/A038862/b038862.txt">Table of n, a(n) for n = 1..10000</a>
%p A038862 filter:= proc(n) local t,y,r;
%p A038862   for t in sort(convert(numtheory:-divisors(n),list))  do
%p A038862     r:= 12*n*t-3*t^4;
%p A038862     if r < 0 then return false fi;
%p A038862     if not issqr(r) then next fi;
%p A038862     y:= (sqrt(r)-3*t^2)/(6*t);
%p A038862     if y::posint then return true fi
%p A038862   od;
%p A038862   false
%p A038862 end proc:
%p A038862 select(filter, [seq(i,i=7..10000,10)]); # _Robert Israel_, Aug 08 2019
%t A038862 With[{nn=60},Select[Union[#[[2]]-#[[1]]&/@Subsets[Range[nn]^3,{2}]],Mod[#,10] == 7&&#<nn^3-(nn-1)^3&]] (* _Harvey P. Dale_, Jan 12 2022 *)
%Y A038862 Cf. A181123.
%K A038862 nonn,base
%O A038862 1,1
%A A038862 _Jeff Burch_
%E A038862 Name corrected by _Robert Israel_, Aug 08 2019