login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054753 Numbers which are the product of a prime and the square of a different prime. 28
12, 18, 20, 28, 44, 45, 50, 52, 63, 68, 75, 76, 92, 98, 99, 116, 117, 124, 147, 148, 153, 164, 171, 172, 175, 188, 207, 212, 236, 242, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428, 436, 452 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A178254(a(n)) = 4; union of A095990 and A096156 [From Reinhard Zumkeller, May 24 2010]

Restated second part of above comment [From Daniel Forgues, Feb 05 2011]:

  Numbers with prime signature (2,1) = union of numbers with ordered prime signature (1,2) and numbers with ordered prime signature (2,1).

A056595(a(n)) = 4. [Reinhard Zumkeller, Aug 15 2011]

Sum(n>=1, 1/a(n)^k) = P(k) * P(2*k) - P(3*k), where P is Prime Zeta function. - Enrique Pérez Herrero, Jun 27 2012

Also numbers n with A001222(n)=3 and A001221(n)=2. - Enrique Pérez Herrero, Jun 27 2012

A089233(a(n)) = 2. - Reinhard Zumkeller, Sep 04 2013

Numbers of the form p^2*q, with p,q distinct primes.  Subsequence of the Triprimes (A014612).  If a(n) is even, then a(n)/2 is semiprime (A001358). - Wesley Ivan Hurt, Sep 08 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

StackExchange, Sequence of numbers with prime factorization pq^2

FORMULA

Solutions of the equation tau(n^5)=11*tau(n). - Paolo P. Lava, Mar 15 2013

EXAMPLE

a(1)=12 because 12=3*2*2.

MAPLE

with(numtheory);

A054753:=proc(q) local n;

for n from 1 to q do if tau(n^5)=11*tau(n) then print(n); fi; od; end:

A054753(10^10);  # Paolo P. Lava, Mar 15 2013

MATHEMATICA

Select[Range[12, 452], {1, 2}==Sort[Last/@FactorInteger[ # ]]&] (* Zak Seidov, Jul 19 2009 *)

CROSSREFS

Numbers with 6 divisors (A030515) which are not 5th powers of primes (A050997).

Sequence in context: A072588 A187039 A072357 * A098899 A098770 A181487

Adjacent sequences:  A054750 A054751 A054752 * A054754 A054755 A054756

KEYWORD

nonn

AUTHOR

Henry Bottomley, Apr 25 2000

EXTENSIONS

Link added and incorrect Mathematica code removed by David Bevan, Sep 17 2011

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 22 18:36 EST 2014. Contains 249807 sequences.