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A054753
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Numbers which are the product of a prime and the square of a different prime.
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26
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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
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1,1
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COMMENTS
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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 5 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
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..1000
StackExchange, Sequence of numbers with prime factorization pq^2
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FORMULA
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Solutions of the equation tau(n^5)=11*tau(n). - Paolo P. Lava, Mar 15 2013
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EXAMPLE
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a(1)=12 because 12=3*2*2.
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MAPLE
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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
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MATHEMATICA
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Select[Range[12, 452], {1, 2}==Sort[Last/@FactorInteger[ # ]]&] (* Zak Seidov, Jul 19 2009 *)
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CROSSREFS
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Cf. 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
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Apr 25 2000
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EXTENSIONS
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Link added and incorrect Mathematica code removed by David Bevan, Sep 17 2011
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STATUS
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approved
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