OFFSET
0,159
LINKS
FORMULA
a(n) = [x^n y^6] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
MAPLE
A025459 := proc(n)
local a, x, y, z, u, v, wcu ;
a := 0 ;
for x from 1 do
if 6*x^3 > n then
return a;
end if;
for y from x do
if x^3+5*y^3 > n then
break;
end if;
for z from y do
if x^3+y^3+4*z^3 > n then
break;
end if;
for u from z do
if x^3+y^3+z^3+3*u^3 > n then
break;
end if;
for v from u do
if x^3+y^3+z^3+u^3+2*v^3 > n then
break;
end if;
wcu := n-x^3-y^3-z^3-u^3-v^3 ;
if isA000578(wcu) then
a := a+1 ;
end if;
end do:
end do:
end do:
end do:
end do:
end proc: # R. J. Mathar, Sep 15 2015
# Alternative:
N:= 200:
G:= mul(1/(1-y*x^(k^3)), k=1..floor(N^(1/3))):
C6:= coeff(series(G, y, 7), y, 6):
S:= series(C6, x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, May 10 2020
MATHEMATICA
a[n_] := Count[PowersRepresentations[n, 6, 3], pr_List /; FreeQ[pr, 0]];
a /@ Range[0, 200] (* Jean-François Alcover, Jun 22 2020 *)
Table[Count[IntegerPartitions[n, {6}], _?(AllTrue[Surd[#, 3], IntegerQ]&)], {n, 0, 110}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 06 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved