A046412 Lengths of nonsquarefree repunits.

9, 18, 22, 27, 36, 42, 44, 45, 54, 63, 66, 72, 78, 81, 84, 88, 90, 99, 108, 110, 111, 117, 126, 132, 135, 144, 153, 154, 156, 162, 168, 171, 176, 180, 189, 198, 205, 207, 210, 216, 220, 222, 225, 234, 242, 243, 252, 261, 264, 270, 272, 279, 286, 288, 294, 297, 306, 308, 312, 315, 324, 330, 333, 336, 342, 351, 352

Offset: 1

Author

Patrick De Geest, Jul 15 1998

Keywords

• nonn
• base

Comments

This is the set of all positive multiples of all positive members of A087094. What is the asymptotic density of this set? - Jeppe Stig Nielsen, Dec 28 2015

Links

• Patrick De Geest, Repunits prime factors
• Shyam Sunder Gupta, Repunit Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 11, 327-352.
• Eric Weisstein's World of Mathematics, Repunit

Crossrefs

Cf. A000042, A004022, A046053, A084006, A087094.

Programs

Maple

remove(t -> numtheory:-issqrfree((10^t-1)/9), [$1..90]); # Robert Israel, Dec 30 2015

Mathematica

Select[Range[300],!SquareFreeQ[(10^#-1)/9]&] (* Harvey P. Dale, Jun 26 2013 *)

PARI

isok(n) = ! issquarefree((10^n-1)/9); \\ Michel Marcus, Dec 31 2015

Formula

a(n)=k where (10^k-1)/9 is not squarefree. - Ray Chandler, Aug 10 2003

Extensions

Terms to a(60) from Ray Chandler, Aug 10 2003

a(61)-a(67) from Max Alekseyev, Apr 29 2022