A179746 - OEIS

%I #21 May 05 2023 10:13:12

%S 3600,7056,8100,15876,17424,19600,22500,24336,39204,41616,48400,51984,

%T 54756,67600,76176,86436,93636,94864,99225,115600,116964,121104,

%U 122500,132496,138384,144400,171396,197136,211600,226576,240100,242064,245025

%N Numbers of the form p^4*q^2*r^2 where p, q, and r are distinct primes.

%C Numbers k such that tau(k^2)/tau(k) = 5 where tau(n) is the number of divisors of n (A000005). - _Bernard Schott_, Nov 27 2020

%H T. D. Noe, <a href="/A179746/b179746.txt">Table of n, a(n) for n = 1..1000</a>

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>

%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(4) - P(4)^2)/2 - P(2)*P(6) + P(8) = 0.00125114..., where P is the prime zeta function. - _Amiram Eldar_, Jul 03 2022

%F a(n) = A085987(n)^2. - _R. J. Mathar_, May 05 2023

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,2,4}; Select[Range[200000],f]

%o (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\36)^(1/4), t1=p^4;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 24 2011

%Y Subsequence of A217584.

%Y Cf. A189988 (tau(k^2)/tau(k) = 3).

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 25 2010