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 A189988 Numbers with prime factorization p^2*q^4. 8

%I

%S 144,324,400,784,1936,2025,2500,2704,3969,4624,5625,5776,8464,9604,

%T 9801,13456,13689,15376,21609,21904,23409,26896,29241,29584,30625,

%U 35344,42849,44944,55696,58564,59536,60025,68121,71824,75625,77841

%N Numbers with prime factorization p^2*q^4.

%C Numbers k such that tau(k^2)/tau(k) = 3 where tau(n) is the number of divisors of n (A000005). - _Michel Marcus_, Feb 09 2018

%H T. D. Noe, <a href="/A189988/b189988.txt">Table of n, a(n) for n = 1..1000</a>

%H W. 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)*P(4) - P(6) = A085548 * A085964 - A085966 = 0.017749..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,4}; Select[Range[150000],f]

%t Module[{upto=80000},Select[Union[Flatten[{#[[1]]^2 #[[2]]^4,#[[1]]^4 #[[2]]^2}&/@ Subsets[Prime[Range[Sqrt[upto/16]]],{2}]]],#<=upto&]] (* _Harvey P. Dale_, Dec 15 2017 *)

%o (PARI) list(lim)=my(v=List(),t);forprime(p=2, (lim\4)^(1/4), t=p^4;forprime(q=2, sqrt(lim\t), if(p==q, next);listput(v,t*q^2))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011

%Y Cf. A178740.

%Y Cf. A085548, A085964, A085966.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 03 2011

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Last modified June 25 04:06 EDT 2021. Contains 345451 sequences. (Running on oeis4.)