A179746 Numbers of the form p^4*q^2*r^2 where p, q, and r are distinct primes.

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

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