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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
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved