A167171 Squarefree semiprimes together with primes.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 29 2009

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

Cf. A000005, A001221.

Programs

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 *)

PARI

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

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

Extensions

Corrected by R. J. Mathar, Oct 31 2009

New name from Charles R Greathouse IV, Apr 05 2017