A303373 Numbers of the form a^3 + b^6, with integers a, b > 0.

2, 9, 28, 65, 72, 91, 126, 128, 189, 217, 280, 344, 407, 513, 576, 730, 737, 756, 793, 854, 945, 1001, 1064, 1072, 1241, 1332, 1395, 1458, 1729, 1792, 2060, 2198, 2261, 2457, 2745, 2808, 2926, 3376, 3439, 3473, 4097, 4104, 4123, 4160, 4221, 4312, 4439, 4608, 4825, 4914

Offset

1,1

Comments

A subsequence of the numbers of the form a^3 + b^2, A055394.

Although it is easy to produce many terms of this sequence, it is nontrivial to check whether a very large number is of this form.

Links

Table of n, a(n) for n=1..50.

Example

The first terms are 1^3 + 1^6 = 2, 2^3 + 1^6 = 9, 3^3 + 1^6 = 28, 4^3 + 1^6 = 65, 2^3 + 2^6 = 72, 3^3 + 2^6 = 91, 5^3 + 1^6 = 126, 4^3 + 2^6 = 128, ...

Prog

(PARI) is(n, k=3, m=6)=for(b=1, sqrtnint(n-1, m), ispower(n-b^m, k)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
A303373_vec(L=10^5, k=3, m=6, S=List())={for(a=1, sqrtnint(L-1, m), for(b=1, sqrtnint(L-a^m, k), listput(S, a^m+b^k))); Set(S)} \\ List of all terms up to limit L

Crossrefs

Cf. A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).

Cf. A303372 (a^2 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).

Sequence in context: A202679 A340049 A256467 * A001093 A248658 A121643

Adjacent sequences: A303370 A303371 A303372 * A303374 A303375 A303376

Keyword

nonn,easy

Author

M. F. Hasler, Apr 22 2018

Status

approved