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A144146 A positive integer n is included if every nonzero exponent in the prime factorization of n is coprime to n. 3

%I

%S 1,2,3,5,6,7,8,9,10,11,13,14,15,17,19,21,22,23,25,26,29,30,31,32,33,

%T 34,35,37,38,39,40,41,42,43,45,46,47,49,51,53,55,56,57,58,59,61,62,63,

%U 65,66,67,69,70,71,73,74,75,77,78,79,81,82,83,85,86,87,88,89,91,93,94,95

%N A positive integer n is included if every nonzero exponent in the prime factorization of n is coprime to n.

%C 1 is included somewhat arbitrarily. 1 has no nonzero exponents in its prime factorization, but it also has no prime factorization exponents that are not coprime to 1.

%H Robert Israel, <a href="/A144146/b144146.txt">Table of n, a(n) for n = 1..10000</a>

%e 40 has the prime-factorization 2^3 * 5^1. The exponents are therefore 3 and 1. Since both 3 and 1 are coprime to 40, then 40 is included in the sequence.

%p filter:= proc(n) local E;

%p E:= map(t -> t[2], ifactors(n)[2]);

%p andmap(t -> igcd(t,n)=1, E)

%p end proc:

%p select(filter, [$1..200]); # _Robert Israel_, Oct 24 2019

%t Select[Range[100], GCD[Times @@ Table[FactorInteger[ # ][[i, 2]], {i, 1, Length[FactorInteger[ # ]]}], # ] == 1 &] (* _Stefan Steinerberger_, Sep 15 2008 *)

%K nonn

%O 1,2

%A _Leroy Quet_, Sep 11 2008

%E More terms from _Stefan Steinerberger_, Sep 15 2008

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Last modified December 5 09:35 EST 2020. Contains 338945 sequences. (Running on oeis4.)