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 A179746 Numbers of the form p^4*q^2*r^2 where p, q, and r are distinct primes. 4
 3600, 7056, 8100, 15876, 17424, 19600, 22500, 24336, 39204, 41616, 48400, 51984, 54756, 67600, 76176, 86436, 93636, 94864, 99225, 115600, 116964, 121104, 122500, 132496, 138384, 144400, 171396, 197136, 211600, 226576, 240100, 242064, 245025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Will Nicholes, Prime Signatures Index to sequences related to prime signature FORMULA 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 a(n) = A085987(n)^2. - R. J. Mathar, May 05 2023 MATHEMATICA f[n_]:=Sort[Last/@FactorInteger[n]]=={2, 2, 4}; Select[Range[200000], f] PROG (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 CROSSREFS Subsequence of A217584. Cf. A189988 (tau(k^2)/tau(k) = 3). Sequence in context: A216682 A348521 A175752 * A096472 A306492 A364990 Adjacent sequences: A179743 A179744 A179745 * A179747 A179748 A179749 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Jul 25 2010 STATUS approved

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Last modified December 6 16:13 EST 2023. Contains 367612 sequences. (Running on oeis4.)