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Squarefree semiprimes together with primes.
26

%I #26 Apr 05 2017 11:00:01

%S 2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,

%T 41,43,46,47,51,53,55,57,58,59,61,62,65,67,69,71,73,74,77,79,82,83,85,

%U 86,87,89,91,93,94,95,97,101,103,106,107,109,111,113,115,118,119,122,123

%N Squarefree semiprimes together with primes.

%C Numbers such that d(n)=2*omega(n), where d = A000005 is the number of divisors.

%C Numbers n such that half of number of divisors of n is equal to number of distinct primes dividing n.

%C Numbers p*q such that p is 1 or a prime and q is a prime greater than p.

%H Felix Fröhlich, <a href="/A167171/b167171.txt">Table of n, a(n) for n = 1..9999</a>

%F Equals A037143 \ A000290 = A006881 union A000040. - _V. Raman_, Sep 13 2012

%F a(n) ~ n log n/log log n. - _Charles R Greathouse IV_, Apr 05 2017

%e a(1)=2 (d(2)=2*omega(2)); a(2)=3 (d(3)=2*omega(3)).

%p omega := proc(n) if n = 1 then 0 ; else nops( numtheory[factorset](n)) ; end if; end proc: isA167171 := proc(n) numtheory[tau](n) = 2*omega(n) ; end proc: for n from 1 to 300 do if isA167171(n) then printf("%d,",n) ; end if ; end do: # _R. J. Mathar_, Oct 31 2009

%t a = {}; Do[If[1 <= PrimeOmega[n] <= 2 && SquareFreeQ[n], AppendTo[a, n]], {n, 123}]; a (* _L. Edson Jeffery_, Jan 01 2015 *)

%o (PARI) for(n=1, 1e3, if(numdiv(n)==2*omega(n), print1(n, ", "))) \\ _Felix Fröhlich_, Aug 11 2014

%Y Cf. A000005, A001221.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 29 2009

%E Corrected by _R. J. Mathar_, Oct 31 2009

%E New name from _Charles R Greathouse IV_, Apr 05 2017