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A085397 Numbers that are not perfect powers and whose squarefree part is not congruent to 1 (mod 4). 2
2, 3, 6, 7, 10, 11, 12, 14, 15, 18, 19, 22, 23, 24, 26, 28, 30, 31, 34, 35, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 54, 55, 56, 58, 59, 60, 62, 63, 66, 67, 70, 71, 72, 74, 75, 76, 78, 79, 82, 83, 86, 87, 88, 90, 91, 92, 94, 95, 96, 98, 99, 102, 103, 104, 106, 107, 108 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contains A016825. - Robert Israel, Mar 20 2016

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Eric Weisstein's World of Mathematics, Artin's Constant

MAPLE

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

  F:= ifactors(n)[2];

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

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

  x mod 4 <> 1;

end proc:

select(f, [$1..200]); # Robert Israel, Mar 20 2016

MATHEMATICA

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 *)

PROG

(PARI) isok(n) = !ispower(n) && ((core(n) % 4) != 1); \\ Michel Marcus, Mar 19 2016

CROSSREFS

Subsequence of A007916.

Cf. A016825.

Sequence in context: A006877 A263881 A208892 * A073439 A188084 A242750

Adjacent sequences:  A085394 A085395 A085396 * A085398 A085399 A085400

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 27 2003

STATUS

approved

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Last modified March 22 22:03 EDT 2017. Contains 283901 sequences.