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

1,2

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

Links

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

Example

66 and 6666 are members but 666 is not.

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

Prog

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

Crossrefs

Cf. A002275, A005117, A010785, A087094.

Sequence in context: A273524 A098959 A071251 * A101730 A276692 A169829

Adjacent sequences: A077568 A077569 A077570 * A077572 A077573 A077574

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 11 2002

Extensions

Corrected and extended by Ray Chandler, Aug 12 2003

Offset changed by Robert Israel, Feb 26 2019

Status

approved