cp's OEIS Frontend

A077571 Squarefree numbers obtained by repeating a single digit.

%I A077571 #20 Nov 02 2019 03:32:30
%S A077571 1,2,3,5,6,7,11,22,33,55,66,77,111,222,555,777,1111,2222,3333,5555,
%T A077571 6666,7777,11111,22222,33333,55555,66666,77777,111111,222222,555555,
%U A077571 1111111,2222222,3333333,5555555,6666666,7777777,11111111,22222222,33333333
%N A077571 Squarefree numbers obtained by repeating a single digit.
%C A077571 From _Robert Israel_, Feb 26 2019: (Start)
%C A077571 If A002275(n) is not in the sequence, then there are no terms of length n.
%C A077571 2*A002275(n) and 5*A002275(n) are in the sequence if and only if A002275(n) is in the sequence.
%C A077571 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.
%C A077571 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)
%C A077571 Intersection of A005117 and A010785. - _Felix Fröhlich_, Feb 26 2019
%H A077571 Robert Israel, <a href="/A077571/b077571.txt">Table of n, a(n) for n = 1..326</a>
%e A077571 66 and 6666 are members but 666 is not.
%p A077571 g:= proc(n) local r;
%p A077571   r:= (10^n-1)/9;
%p A077571   if not numtheory:-issqrfree(r) then NULL
%p A077571   elif n mod 6 = 0 then r, 2*r, 5*r
%p A077571   elif n mod 3 = 0 then r, 2*r, 5*r, 7*r
%p A077571   else r, 2*r, 3*r,5*r, 6*r, 7*r
%p A077571   fi
%p A077571 end proc:
%p A077571 seq(g(n),n=1..10); # _Robert Israel_, Feb 26 2019
%o A077571 (PARI) is(n) = n>0 && vecmin(digits(n))==vecmax(digits(n)) && issquarefree(n) \\ _Felix Fröhlich_, Feb 26 2019
%Y A077571 Cf. A002275, A005117, A010785, A087094.
%K A077571 base,easy,nonn
%O A077571 1,2
%A A077571 _Amarnath Murthy_, Nov 11 2002
%E A077571 Corrected and extended by _Ray Chandler_, Aug 12 2003
%E A077571 Offset changed by _Robert Israel_, Feb 26 2019