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Numbers n such that the number of distinct primes dividing n is a square.
1

%I #11 Mar 20 2013 03:47:29

%S 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,

%T 59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,128,

%U 131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,210,211,223,227,229,233,239,241,243,251,256,257,263,269,271,277,281

%N Numbers n such that the number of distinct primes dividing n is a square.

%H Enrique Pérez Herrero, <a href="/A036116/b036116.txt">Table of n, a(n) for n = 1..5000</a>

%e 8 = 2^3 is divisible by just one (distinct) prime, 2 and 1 is a square, so 8 is in the sequence.

%p readlib(issqr): with(numtheory): select(x->issqr(nops(factorset(x))),[ seq(n,n=1..300) ]);

%t Select[Range[100],IntegerQ[PrimeNu[#]^(1/2)]&] (* _Enrique Pérez Herrero_, Jul 07 2012 *)

%o (PARI) is(n)=issquare(omega(n)) \\ _Charles R Greathouse IV_, Mar 19 2013

%Y Differs from A000961 at a(62) = 210, etc.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.