

A167171


Squarefree semiprimes together with primes.


8



2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 67, 69, 71, 73, 74, 77, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 115, 118, 119, 122, 123
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OFFSET

1,1


COMMENTS

Numbers such that d(n)=2*omega(n), where d = A000005 is the number of divisors.
Numbers n such that half of number of divisors of n is equal to number of distinct primes dividing n.
Numbers p*q such that p is 1 or a prime and q is a prime greater than p.


LINKS

Felix Fröhlich, Table of n, a(n) for n = 1..9999


FORMULA

Equals A037143 \ A000290 = A006881 union A000040.  V. Raman, Sep 13 2012
a(n) ~ n log n/log log n.  Charles R Greathouse IV, Apr 05 2017


EXAMPLE

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


MAPLE

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


MATHEMATICA

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


PROG

(PARI) for(n=1, 1e3, if(numdiv(n)==2*omega(n), print1(n, ", "))) \\ Felix Fröhlich, Aug 11 2014


CROSSREFS

Cf. A000005, A001221.
Sequence in context: A284892 A319315 A301899 * A087008 A302798 A294472
Adjacent sequences: A167168 A167169 A167170 * A167172 A167173 A167174


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Oct 29 2009


EXTENSIONS

Corrected by R. J. Mathar, Oct 31 2009
New name from Charles R Greathouse IV, Apr 05 2017


STATUS

approved



