A337529 Numbers that are the sum of two of their cubed divisors (not necessarily distinct).

2, 16, 54, 72, 128, 250, 432, 520, 576, 686, 756, 1024, 1458, 1944, 2000, 2662, 3456, 4160, 4394, 4608, 5488, 6048, 6750, 7560, 8192, 9000, 9826, 11664, 13718, 14040, 15552, 15750, 16000, 18522, 19656, 19710, 20412, 21296, 24334, 24696, 27648, 31250, 32832, 33280

Offset

1,1

Comments

All terms are even. - Alois P. Heinz, Aug 30 2020

Numbers of the form a^3 + b^3 where a divides b^3 and b divides a^3. - Robert Israel, Nov 01 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

16 is in the sequence since 2 is a divisor of 16 and 2^3 + 2^3 = 16.

Maple

q:= n-> (s-> ormap(x-> n-x in s, s))(map(x-> x^3, numtheory[divisors](n))):
select(q, [2*i$i=1..17000])[];  # Alois P. Heinz, Aug 30 2020
N:= 50000: # to get terms <= N
R:= NULL:
for a from 1 to floor(N^(1/3)) do
  Bs:= select(b -> b^3 + a^3 <= N and b^3 mod a = 0, numtheory:-divisors(a^3));
  R:= R union map(b -> a^3 + b^3, Bs);
od:
sort(convert(R, list)); # Robert Israel, Nov 01 2020

Mathematica

M = 40000; (* to get terms <= M *)
R = {};
For[a = 1, a <= Floor[M^(1/3)], a++,
     Bs = Select[Divisors[a^3], #^3 + a^3 <= M && Mod[#^3, a] == 0&];
     R = Union[R, a^3 + #^3& /@ Bs]];
Sort[R] (* Jean-François Alcover, Jan 01 2022, after Robert Israel *)

Crossrefs

Cf. A094147 (sum of two squared divisors).

Sequence in context: A220139 A027273 A210710 * A225051 A033431 A107610

Adjacent sequences: A337526 A337527 A337528 * A337530 A337531 A337532

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 30 2020

Extensions

a(12)-a(44) from Alois P. Heinz, Aug 30 2020

Status

approved