A069821 a(n) is the smallest k > n such that (k^3 - 1)/(n^3 - 1) is an integer.

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 211, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 466, 1369, 1444, 1075, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601

Offset

2,1

Comments

For almost all n, a(n) = n^2. Exceptions: a(16) = 211, a(36) = 466, a(39) = 1075, a(53) = 1173, a(58) = 919...

Links

Jinyuan Wang, Table of n, a(n) for n = 2..1000

Prog

(PARI) a(n) = {k=n+1; while((k^3-1)%(n^3-1)>0, k++); k; } \\ Jinyuan Wang, Jul 29 2019
(Magma) sol:=[]; m:=1; for n in [2..50] do for k in [n+1..3000] do if IsIntegral((k^3-1)/(n^3-1)) then  sol[m]:=k;  m:=m+1; break; end if; end for; end for; sol; // Marius A. Burtea, Jul 30 2019

Crossrefs

Sequence in context: A162497 A216500 A370785 * A331221 A376170 A174452

Adjacent sequences: A069818 A069819 A069820 * A069822 A069823 A069824

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 28 2002

Extensions

Name clarified by Jon E. Schoenfield, Jul 28 2019

Status

approved