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

1,1

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: A301899 A325398 A325399 * A087008 A326537 A302798

Adjacent sequences: A167168 A167169 A167170 * A167172 A167173 A167174

Keyword

nonn

Author

Juri-Stepan 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