login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085397 Numbers that are not perfect powers and whose squarefree part is not congruent to 1 (mod 4). 2

%I

%S 2,3,6,7,10,11,12,14,15,18,19,22,23,24,26,28,30,31,34,35,38,39,40,42,

%T 43,44,46,47,48,50,51,54,55,56,58,59,60,62,63,66,67,70,71,72,74,75,76,

%U 78,79,82,83,86,87,88,90,91,92,94,95,96,98,99,102,103,104,106,107,108

%N Numbers that are not perfect powers and whose squarefree part is not congruent to 1 (mod 4).

%C Contains A016825. - _Robert Israel_, Mar 20 2016

%H T. D. Noe, <a href="/A085397/b085397.txt">Table of n, a(n) for n=1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArtinsConstant.html">Artin's Constant</a>

%p f:= proc(n) local F,x;

%p F:= ifactors(n)[2];

%p if igcd(seq(f[2],f=F)) > 1 then return false fi;

%p x:= mul(f[1], f = select(t -> t[2]::odd, F));

%p x mod 4 <> 1;

%p end proc:

%p select(f, [$1..200]); # _Robert Israel_, Mar 20 2016

%t fi[n_] := fi[n] = FactorInteger[n]; perfectPowerQ[n_] := Length[uf = Union[ fi[n][[All, 2]]]] == 1 && uf[[1]] >= 2; SquareFreePart[n_] := Times @@ Apply[Power, ({#[[1]], Mod[#[[2]], 2]} & ) /@ fi[n], {1}]; ok[n_] := ! perfectPowerQ[n] && Mod[ SquareFreePart[n], 4] != 1; Select[ Range[110], ok] (* _Jean-Fran├žois Alcover_, Jan 20 2012 *)

%o (PARI) isok(n) = !ispower(n) && ((core(n) % 4) != 1); \\ _Michel Marcus_, Mar 19 2016

%Y Subsequence of A007916.

%Y Cf. A016825.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jun 27 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 7 19:13 EST 2021. Contains 341928 sequences. (Running on oeis4.)