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A337529
Numbers that are the sum of two of their cubed divisors (not necessarily distinct).
1
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 30 2020
EXTENSIONS
a(12)-a(44) from Alois P. Heinz, Aug 30 2020
STATUS
approved