[go: up one dir, main page]

login
A167171
Squarefree semiprimes together with primes.
26
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
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
Sequence in context: A301899 A325398 A325399 * A087008 A326537 A302798
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected by R. J. Mathar, Oct 31 2009
New name from Charles R Greathouse IV, Apr 05 2017
STATUS
approved