A077571 Squarefree numbers obtained by repeating a single digit.

1, 2, 3, 5, 6, 7, 11, 22, 33, 55, 66, 77, 111, 222, 555, 777, 1111, 2222, 3333, 5555, 6666, 7777, 11111, 22222, 33333, 55555, 66666, 77777, 111111, 222222, 555555, 1111111, 2222222, 3333333, 5555555, 6666666, 7777777, 11111111, 22222222, 33333333

Offset: 1

Author

Amarnath Murthy, Nov 11 2002

Keywords

• base
• easy
• nonn

Comments

From Robert Israel, Feb 26 2019: (Start)

If A002275(n) is not in the sequence, then there are no terms of length n.

2*A002275(n) and 5*A002275(n) are in the sequence if and only if A002275(n) is in the sequence.

3*A002275(n) and 6*A002275(n) are in the sequence if and only if A002275(n) is in the sequence and n is not divisible by 3.

7*A002275(n) is in the sequence if and only if A002275(n) is in the sequence and n is not divisible by 6. (End)

Intersection of A005117 and A010785. - Felix Fröhlich, Feb 26 2019

Examples

			66 and 6666 are members but 666 is not.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..326

Crossrefs

Cf. A002275, A005117, A010785, A087094.

Programs

Maple

g:= proc(n) local r;
  r:= (10^n-1)/9;
  if not numtheory:-issqrfree(r) then NULL
  elif n mod 6 = 0 then r, 2*r, 5*r
  elif n mod 3 = 0 then r, 2*r, 5*r, 7*r
  else r, 2*r, 3*r,5*r, 6*r, 7*r
  fi
end proc:
seq(g(n),n=1..10); # Robert Israel, Feb 26 2019

PARI

is(n) = n>0 && vecmin(digits(n))==vecmax(digits(n)) && issquarefree(n) \\ Felix Fröhlich, Feb 26 2019

Extensions

Corrected and extended by Ray Chandler, Aug 12 2003

Offset changed by Robert Israel, Feb 26 2019