A189715 - OEIS

%I #15 Mar 08 2021 02:48:35

%S 1,4,6,7,9,10,13,15,16,19,22,24,25,28,31,33,34,36,37,40,42,43,46,49,

%T 51,52,54,55,58,60,61,63,64,67,69,70,73,76,78,79,81,82,85,87,88,90,91,

%U 94,96,97,100,103,105,106,109,112,114,115,117,118,121,123,124,127,130,132,133,135,136,139,141,142,144,145,148,150,151,154,157,159

%N Numbers k such that A156595(k-1) = 0; complement of A189716.

%C See A156595.

%C Numbers whose squarefree part is congruent modulo 9 to 1, 4, 6 or 7. - _Peter Munn_, May 17 2020

%C The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Mar 08 2021

%H Amiram Eldar, <a href="/A189715/b189715.txt">Table of n, a(n) for n = 1..10000</a>

%t t = Nest[Flatten[# /. {0->{0,1,1}, 1->{0,1,0}}] &, {0}, 5] (*A156595*)

%t f[n_] := t[[n]]

%t Flatten[Position[t, 0]] (*A189715*)

%t Flatten[Position[t, 1]] (*A189716*)

%t s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;

%t Table[s[n], {n, 1, 120}] (*A189717*)

%t f[p_, e_] := (p^Mod[e, 2]); sqfpart[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[160], MemberQ[{1, 4, 6, 7}, Mod[sqfpart[#], 9]] &] (* _Amiram Eldar_, Mar 08 2021 *)

%Y Cf. A007913, A156595, A189716, A189717.

%Y Union of A055040 and A055047.

%K nonn

%O 1,2

%A _Clark Kimberling_, Apr 26 2011

%E Name enhanced by _Peter Munn_, May 17 2020