

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
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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 *)
With[{nn=60}, Take[Union[Flatten[{#[[1]]#[[2]]^2, #[[1]]^2 #[[2]]}&/@ Subsets[ Prime[Range[nn]], {2}]]], nn]] (* Harvey P. Dale, Dec 15 2014 *)


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,changed


AUTHOR

Henry Bottomley, Apr 25 2000


EXTENSIONS

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


STATUS

approved



