A174897 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.

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, 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, 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

Offset: 1

Author

Jaroslav Krizek, Apr 01 2010

Keywords

• nonn

Comments

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for characteristic functions

Crossrefs

Cf. A007955, A174895, A174898.

Programs

Mathematica

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 *)

PARI

up_to = 65537;
v174897 = vector(up_to);
A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ This function from Charles R Greathouse IV, Feb 11 2011
for(k=1, up_to, t=A007955(k); if(t<=up_to, v174897[t] = 1));
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
write_to_bfile(1,v174897,"b174897_upto65537.txt");
\\ Antti Karttunen, Oct 20 2017

Formula

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

Extensions

Name edited and more terms added by Antti Karttunen, Oct 20 2017