A181375 - OEIS

%I #20 Feb 12 2024 02:35:17

%S 2,9,41,202,938,4354,20330,94625,439959,2045048,9500746,44124084,

%T 204883131,951202028,4415710979,20497646229,95146359635

%N Total number of positive integers below 10^n requiring 2 positive cubes in their representation as sum of cubes.

%C A061439(n) + a(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + A181402(n) + A181404(n) + A130130(n) = A002283(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WaringsProblem.html">Waring's Problem</a>.

%p iscube:=proc(n) if root(n,3)=trunc(root(n,3)) then true; else false; fi; end:

%p isA003325:=proc(n) local x,y3; if iscube(n) then false; else for x from 1 do y3:=n-x^3; if y3<x^3 then return false; elif iscube(y3) then return true; fi; od; fi; end:

%p a:=proc(n) local i,k; i:=0; for k from 2 to 10^n-1 do if isA003325(k) then i:=i+1; fi; od: return(i); end:

%p for n from 1 do print(a(n)); od;

%o (PARI) a(n)=my(N=10^n,v=List(),x3);sum(x=1,sqrtnint(N-1,3),x3=x^3;sum(y=1, min(sqrtnint(N-x3,3),x), !ispower(x3+y^3,3) && listput(v,x3+y^3))); #vecsort(v,,8) \\ _Charles R Greathouse IV_, Oct 16 2013

%Y Cf. A003325.

%K nonn,more

%O 1,1

%A _Martin Renner_, Jan 28 2011

%E a(6)-a(12) from _Lars Blomberg_, May 04 2011

%E a(13)-a(17) from _Hiroaki Yamanouchi_, Jul 12 2014