A024667 a(n) = position of 2*n^3 in A003325.

1, 3, 6, 11, 18, 25, 33, 44, 57, 68, 81, 99, 116, 134, 152, 177, 200, 223, 246, 276, 304, 331, 360, 397, 433, 465, 501, 541, 579, 617, 662, 707, 749, 793, 845, 895, 944, 995, 1051, 1105, 1161, 1214, 1279, 1337, 1397, 1456, 1528, 1591, 1657, 1722, 1799, 1870

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A003325.

Programs

Maple

M:= 200: # to get a(1) .. a(M)
N:= 2*N^3:
A:=sort(convert({seq(seq(x^3 + y^3, y = 1 .. floor((N-x^3)^(1/3))),x=1..floor(N^(1/3)))},list)):
filter:= proc(n) local F;
if n::odd then return false fi;
  F:= ifactors(n/2)[2][..,2] mod 3;
  andmap(`=`,F,0)
end proc:
select(t -> filter(A[t]), [$1..nops(A)]); # Robert Israel, Sep 19 2024

Formula

It appears that a(n) ~ 2^(2/3) * Pi^2 * n^2/(9 * Gamma(2/3)^3). - Robert Israel, Sep 19 2024