A085987 - OEIS

%I #37 Feb 09 2024 10:11:28

%S 60,84,90,126,132,140,150,156,198,204,220,228,234,260,276,294,306,308,

%T 315,340,342,348,350,364,372,380,414,444,460,476,490,492,495,516,522,

%U 525,532,550,558,564,572,580,585,620,636,644,650,666,693,708,726

%N Product of exactly four primes, three of which are distinct (p^2*q*r).

%C A014613 is completely determined by A030514, A065036, A085986, A085987 and A046386 since p(4) = 5. (cf. A000041). More generally, the first term of sequences which completely determine the k-almost primes can be found in A036035 (a resorted version of A025487).

%C A050326(a(n)) = 4. - _Reinhard Zumkeller_, May 03 2013

%H T. D. Noe, <a href="/A085987/b085987.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%e a(1) = 60 since 60 = 2*2*3*5 and has three distinct prime factors.

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,2}; Select[Range[2000], f] (* _Vladimir Joseph Stephan Orlovsky_, May 03 2011 *)

%t pefp[{a_,b_,c_}]:={a^2 b c,a b^2 c,a b c^2}; Module[{upto=800},Select[ Flatten[ pefp/@Subsets[Prime[Range[PrimePi[upto/6]]],{3}]]//Union,#<= upto&]] (* _Harvey P. Dale_, Oct 02 2018 *)

%o (PARI) list(lim)=my(v=List(),t,x,y,z);forprime(p=2,lim^(1/4),t=lim\p^2;forprime(q=p+1,sqrtint(t),forprime(r=q+1,t\q,x=p^2*q*r;y=p*q^2*r;listput(v,x);if(y<=lim,listput(v,y);z=p*q*r^2;if(z<=lim,listput(v,z))))));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 15 2011

%o (PARI) is(n)=vecsort(factor(n)[,2]~)==[1,1,2] \\ _Charles R Greathouse IV_, Oct 19 2015

%Y Cf. A001248, A006881, A030078, A054753, A007304, A050997, A046387, A036035, A086974.

%Y Subsequence of A014613, A307341, A178212.

%K nonn

%O 1,1

%A _Alford Arnold_, Jul 08 2003

%E More terms from _Reinhard Zumkeller_, Jul 25 2003