A065202 Characteristic function of A065201: a(n) = if A065201(k) = n for some k then 1 else 0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2001

Keywords

• nonn

Links

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

Crossrefs

Cf. A051119, A053585, A065201, A065200, A070003, A107078.

Programs

Mathematica

a[n_] := If[Max[Most[FactorInteger[n][[;;, 2]]]] > 1, 1, 0]; Array[a, 100] (* Amiram Eldar, Mar 19 2025 *)

PARI

A053585(n) = if(n>1, my(f=factor(n)); f[#f~, 1]^f[#f~, 2], 1) \\ Charles R Greathouse IV, Nov 10 2015
A051119(n) = (n/A053585(n));
A065202(n) = (1-abs(moebius(A051119(n)))); \\ Antti Karttunen, Aug 27 2017

PARI

a(n) = {my(e = factor(n)[,2]); #e > 1 && vecmax(e[1..#e-1]) > 1;} \\ Amiram Eldar, Mar 19 2025

Formula

a(A065200(n)) = 0 and a(A065201(n)) = 1.

a(n) = A107078(A051119(n)). - Antti Karttunen, Aug 27 2017

Extensions

Edited by Franklin T. Adams-Watters, Oct 27 2006