

A144146


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


3



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, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95
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OFFSET

1,2


COMMENTS

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.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

40 has the primefactorization 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.


MAPLE

filter:= proc(n) local E;
E:= map(t > t[2], ifactors(n)[2]);
andmap(t > igcd(t, n)=1, E)
end proc:
select(filter, [$1..200]); # Robert Israel, Oct 24 2019


MATHEMATICA

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


CROSSREFS

Sequence in context: A326947 A256450 A119605 * A284763 A090240 A137407
Adjacent sequences: A144143 A144144 A144145 * A144147 A144148 A144149


KEYWORD

nonn


AUTHOR

Leroy Quet, Sep 11 2008


EXTENSIONS

More terms from Stefan Steinerberger, Sep 15 2008


STATUS

approved



