A077572 Nonsquarefree numbers obtained by repeating a single digit.

4, 8, 9, 44, 88, 99, 333, 444, 666, 888, 999, 4444, 8888, 9999, 44444, 88888, 99999, 333333, 444444, 666666, 777777, 888888, 999999, 4444444, 8888888, 9999999, 44444444, 88888888, 99999999, 111111111, 222222222, 333333333, 444444444

Offset: 1

Author

Amarnath Murthy, Nov 11 2002

Keywords

• base
• easy
• nonn

Examples

			666 and 111111111 are members but 66, 1111 etc. are not.
		

Crossrefs

Cf. A077571, A087094.

Subsequence of A013929 and A035132.

Programs

Mathematica

Select[Flatten[Table[FromDigits[PadRight[{},i,n]],{i,9},{n,9}]],!SquareFreeQ[#]&] (* Harvey P. Dale, Jan 22 2013 *)

Python

from sympy.ntheory.factor_ import core
def repsthru(maxd):
  yield from (int(di*d) for d in range(1, maxd+1) for di in "123456789")
def okrep(r): return r > 3 and core(r, 2) != r
print(list(filter(okrep, repsthru(9)))) # Michael S. Branicky, Apr 08 2021

Extensions

Corrected and extended by Ray Chandler, Aug 12 2003

Offset changed by Andrew Howroyd, Sep 29 2024