A174897 - OEIS

%I #15 Oct 21 2017 21:14:31

%S 1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,

%T 0,1,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,1,0,0,1,0,

%U 0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,0,1,0,0

%N a(n) = characteristic function of numbers k such that A007955(m) = k has solution for some m, where A007955(m) = product of divisors of m.

%C a(n) = characteristic function of numbers from A174895(n).

%C a(n) = 1 if A007955(m) = n for any m, else 0.

%H Antti Karttunen, <a href="/A174897/b174897.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = 1 - A174898(n).

%t Block[{nn = 105, t}, t = ConstantArray[0, nn]; ReplacePart[t, Map[# -> 1 &, TakeWhile[Sort@ Array[Times @@ Divisors@ # &, nn], # <= 105 &]]]] (* _Michael De Vlieger_, Oct 20 2017 *)

%o (PARI)

%o up_to = 65537;

%o v174897 = vector(up_to);

%o A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ This function from _Charles R Greathouse IV_, Feb 11 2011

%o for(k=1, up_to, t=A007955(k); if(t<=up_to, v174897[t] = 1));

%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o write_to_bfile(1,v174897,"b174897_upto65537.txt");

%o \\ _Antti Karttunen_, Oct 20 2017

%Y Cf. A007955, A174895, A174898.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Apr 01 2010

%E Name edited and more terms added by _Antti Karttunen_, Oct 20 2017