A174897 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A007955, A174895, A174898.

Sequence in context: A373834 A132194 A354034 * A316441 A190938 A342653