A190469 - OEIS

%I #15 Mar 07 2024 01:27:56

%S 14400,28224,69696,72900,78400,97344,142884,166464,193600,207936,

%T 270400,304704,352836,379456,462400,484416,492804,529984,553536,

%U 562500,577600,788544,842724,846400,893025,906304,968256,1052676,1065024,1132096

%N Numbers with prime factorization p^2*q^2*r^6 where p, q, and r are distinct primes.

%H T. D. Noe, <a href="/A190469/b190469.txt">Table of n, a(n) for n = 1..1000</a>

%H Will Nicholes, <a href="https://willnicholes.com/2010/06/06/list-of-prime-signatures">List of prime signatures</a>, 2010.

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

%F Sum_{n>=1} 1/a(n) = P(2)^2*P(6)/2 - P(2)*P(8)/2 - P(4)*P(6)/2 - P(2)*P(8) + P(10) = 0.00024535673248061231753..., where P is the prime zeta function. - _Amiram Eldar_, Mar 07 2024

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,2,6}; Select[Range[1600000],f]

%o (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\36)^(1/6), t1=p^6;forprime(q=2, sqrt(lim\t1), if(p==q, next);t2=t1*q^2;forprime(r=q+1, sqrt(lim\t2), if(p==r,next);listput(v,t2*r^2)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011

%Y Cf. A190466, A190467, A190468.

%Y Cf. A085548, A085964, A085966, A085968.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 10 2011