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A123053
Sum of a positive square, a positive cube and a positive fourth power.
3
3, 6, 10, 11, 13, 18, 21, 25, 26, 27, 28, 29, 32, 33, 34, 37, 38, 40, 42, 44, 45, 47, 49, 51, 52, 53, 58, 59, 60, 64, 66, 68, 69, 73, 74, 77, 79, 81, 83, 84, 86, 88, 89, 90, 91, 92, 93, 96, 98, 101, 102, 105, 107, 109, 112, 114, 116, 117, 118, 123, 124, 125
OFFSET
1,1
LINKS
FORMULA
{A000290 \ 0} + {A000578 \ 0} + {A000583}. {a^4 + b^3 + c^2 for a,b,c>0}.
EXAMPLE
a(1) = 3 = 1^4 + 1^3 + 1^2.
a(2) = 6 = 1^4 + 1^3 + 2^2.
a(3) = 10 = 1^4 + 2^3 + 1^2.
a(4) = 11 = 1^4 + 1^3 + 3^2.
a(5) = 13 = 1^4 + 2^3 + 2^2.
a(6) = 18 = 1^4 + 1^3 + 4^2 = 1^4 + 2^3 + 3^2 = 2^4 + 1^3 + 1^2.
MAPLE
isA123053 := proc(n)
local x, y, z ;
for x from 1 do
if x^2 > n then
return false;
end if;
for y from 1 do
if x^2+y^3> n then
break;
end if;
for z from 1 do
if x^2+y^3+z^4 > n then
break;
elif x^2+y^3+z^4 = n then
return true;
end if;
end do:
end do:
end do:
end proc:
n := 1 ;
for c from 0 to 10000 do
if isA123053(c) then
printf("%d %d\n", n, c) ;
n := n+1 ;
end if;
end do: # R. J. Mathar, Sep 07 2020
MATHEMATICA
Select[ Union[ Total /@ Tuples[{Range[64]^2, Range[8]^4, Range[16]^3}]], # < 200 &] (* Giovanni Resta, Jun 12 2016 *)
CROSSREFS
Cf. A000290 (squares), A000578 (cubes), A000583 (4th powers), A055394 (numbers that are the sum of a positive square and a positive cube).
Sequence in context: A043321 A241858 A231668 * A221129 A138289 A219638
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 25 2006
EXTENSIONS
38, 86, and 93 added and 108 deleted by Giovanni Resta, Jun 12 2016
STATUS
approved