cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167171 Squarefree semiprimes together with primes.

This page as a plain text file.
%I A167171 #26 Apr 05 2017 11:00:01
%S A167171 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 A167171 41,43,46,47,51,53,55,57,58,59,61,62,65,67,69,71,73,74,77,79,82,83,85,
%U A167171 86,87,89,91,93,94,95,97,101,103,106,107,109,111,113,115,118,119,122,123
%N A167171 Squarefree semiprimes together with primes.
%C A167171 Numbers such that d(n)=2*omega(n), where d = A000005 is the number of divisors.
%C A167171 Numbers n such that half of number of divisors of n is equal to number of distinct primes dividing n.
%C A167171 Numbers p*q such that p is 1 or a prime and q is a prime greater than p.
%H A167171 Felix Fröhlich, <a href="/A167171/b167171.txt">Table of n, a(n) for n = 1..9999</a>
%F A167171 Equals A037143 \ A000290 = A006881 union A000040. - _V. Raman_, Sep 13 2012
%F A167171 a(n) ~ n log n/log log n. - _Charles R Greathouse IV_, Apr 05 2017
%e A167171 a(1)=2 (d(2)=2*omega(2)); a(2)=3 (d(3)=2*omega(3)).
%p A167171 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 A167171 a = {}; Do[If[1 <= PrimeOmega[n] <= 2 && SquareFreeQ[n], AppendTo[a, n]], {n, 123}]; a (* _L. Edson Jeffery_, Jan 01 2015 *)
%o A167171 (PARI) for(n=1, 1e3, if(numdiv(n)==2*omega(n), print1(n, ", "))) \\ _Felix Fröhlich_, Aug 11 2014
%Y A167171 Cf. A000005, A001221.
%K A167171 nonn
%O A167171 1,1
%A A167171 _Juri-Stepan Gerasimov_, Oct 29 2009
%E A167171 Corrected by _R. J. Mathar_, Oct 31 2009
%E A167171 New name from _Charles R Greathouse IV_, Apr 05 2017