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 A189988 Numbers with prime factorization p^2*q^4. 8
 144, 324, 400, 784, 1936, 2025, 2500, 2704, 3969, 4624, 5625, 5776, 8464, 9604, 9801, 13456, 13689, 15376, 21609, 21904, 23409, 26896, 29241, 29584, 30625, 35344, 42849, 44944, 55696, 58564, 59536, 60025, 68121, 71824, 75625, 77841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 W. Nicholes, Prime Signatures FORMULA 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 MATHEMATICA f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 4}; Select[Range[150000], f] 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 *) PROG (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 CROSSREFS Cf. A178740. Cf. A085548, A085964, A085966. Sequence in context: A335543 A217584 A030633 * A232892 A034285 A211469 Adjacent sequences:  A189985 A189986 A189987 * A189989 A189990 A189991 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, May 03 2011 STATUS approved

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Last modified May 15 08:59 EDT 2021. Contains 343909 sequences. (Running on oeis4.)