|
%I #53 Jul 19 2023 07:43:40
%S 2310,2730,3570,3990,4290,4620,4830,5460,5610,6006,6090,6270,6510,
%T 6630,6930,7140,7410,7590,7770,7854,7980,8190,8580,8610,8778,8970,
%U 9030,9240,9282,9570,9660,9690,9870,10010,10230,10374,10626,10710,10920,11130,11220,11310
%N Numbers that are divisible by exactly 5 different primes.
%H T. D. Noe, <a href="/A051270/b051270.txt">Table of n, a(n) for n = 1..1000</a>
%H Hans Montanus and Ron Westdijk, <a href="https://matharoundtheblock.eu/?page_id=125">Cellular Automation and Binomials</a>, Math around the Block (2022), p. 90.
%e 2730 = 2*3*5*7*13 is the first nontrivial 5-prime factor number following the 5th primorial, 2310 = 2*3*5*7*11.
%p A051270 := proc(n)
%p option remember;
%p local a;
%p if n = 1 then
%p 2*3*5*7*11 ;
%p else
%p for a from procname(n-1)+1 do
%p if A001221(a)= 5 then
%p return a;
%p end if;
%p end do:
%p end if;
%p end proc: # _R. J. Mathar_, Oct 13 2019
%t Select[Range[12000],PrimeNu[#]==5&] (* _Harvey P. Dale_, Feb 13 2012 *)
%o (PARI) is(n)=omega(n)==5 \\ _Charles R Greathouse IV_, Apr 29 2015
%o (PARI) A246655(lim)=my(v=List(primes([2,lim\=1]))); for(e=2,logint(lim,2), forprime(p=2,sqrtnint(lim,e), listput(v,p^e))); Set(v)
%o list(lim,pr=5)=if(pr==1, return(A246655(lim))); my(v=List(),pr1=pr-1,mx=prod(i=1,pr1,prime(i))); forprime(p=prime(pr),lim\mx, my(u=list(lim\p,pr1)); for(i=1,#u,listput(v,p*u[i]))); Set(v) \\ _Charles R Greathouse IV_, Feb 03 2023
%o (Python)
%o from sympy import primefactors
%o print([n for n in range(2, 20001) if len(primefactors(n))==5]) # _Indranil Ghosh_, Apr 06 2017
%Y A046303 is a subsequence.
%Y Row 5 of A125666.
%Y Cf. A000977, A002110.
%K nonn
%O 1,1
%A _Labos Elemer_
|
