|
%I #13 Sep 07 2020 05:58:37
%S 3,6,10,11,13,18,21,25,26,27,28,29,32,33,34,37,38,40,42,44,45,47,49,
%T 51,52,53,58,59,60,64,66,68,69,73,74,77,79,81,83,84,86,88,89,90,91,92,
%U 93,96,98,101,102,105,107,109,112,114,116,117,118,123,124,125
%N Sum of a positive square, a positive cube and a positive fourth power.
%H Giovanni Resta, <a href="/A123053/b123053.txt">Table of n, a(n) for n = 1..10000</a>
%F {A000290 \ 0} + {A000578 \ 0} + {A000583}. {a^4 + b^3 + c^2 for a,b,c>0}.
%e a(1) = 3 = 1^4 + 1^3 + 1^2.
%e a(2) = 6 = 1^4 + 1^3 + 2^2.
%e a(3) = 10 = 1^4 + 2^3 + 1^2.
%e a(4) = 11 = 1^4 + 1^3 + 3^2.
%e a(5) = 13 = 1^4 + 2^3 + 2^2.
%e a(6) = 18 = 1^4 + 1^3 + 4^2 = 1^4 + 2^3 + 3^2 = 2^4 + 1^3 + 1^2.
%p isA123053 := proc(n)
%p local x,y,z ;
%p for x from 1 do
%p if x^2 > n then
%p return false;
%p end if;
%p for y from 1 do
%p if x^2+y^3> n then
%p break;
%p end if;
%p for z from 1 do
%p if x^2+y^3+z^4 > n then
%p break;
%p elif x^2+y^3+z^4 = n then
%p return true;
%p end if;
%p end do:
%p end do:
%p end do:
%p end proc:
%p n := 1 ;
%p for c from 0 to 10000 do
%p if isA123053(c) then
%p printf("%d %d\n",n,c) ;
%p n := n+1 ;
%p end if;
%p end do: # _R. J. Mathar_, Sep 07 2020
%t Select[ Union[ Total /@ Tuples[{Range[64]^2, Range[8]^4, Range[16]^3}]], # < 200 &] (* _Giovanni Resta_, Jun 12 2016 *)
%Y Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A055394 (numbers that are the sum of a positive square and a positive cube).
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Sep 25 2006
%E 38, 86, and 93 added and 108 deleted by _Giovanni Resta_, Jun 12 2016
|
