login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179746 Numbers of the form p^4*q^2*r^2 where p, q, and r are distinct primes. 3
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

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 A250439

Adjacent sequences:  A179743 A179744 A179745 * A179747 A179748 A179749

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 25 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)