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A030515
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Numbers with exactly 6 divisors.
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16
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12, 18, 20, 28, 32, 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, 243, 244, 245, 261, 268, 275, 279, 284, 292, 316, 325, 332, 333, 338, 356, 363, 369, 387, 388, 404, 412, 423, 425, 428
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OFFSET
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1,1
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COMMENTS
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Numbers which are either the 5th power of a prime or the product of a prime and the square of a different prime, i.e., numbers which are in A050997 (5th powers of primes) or A054753. - Henry Bottomley, Apr 25 2000
Also numbers which are the square root of the product of their proper divisors. - Amarnath Murthy, Apr 21 2001
Such numbers are multiplicatively 3-perfect (i.e., the product of divisors of a(n) equals a(n)^3). - Lekraj Beedassy, Jul 13 2005
Since A119479(6)=5, there are never more than 5 consecutive terms. Quintuples of consecutive terms start at 10093613546512321, 14414905793929921, 266667848769941521, ... (A141621). No such quintuple contains a term of the form p^5. - Ivan Neretin, Feb 08 2016
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REFERENCES
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Amarnath Murthy, A note on the Smarandache Divisor sequences, Smarandache Notions Journal, Vol. 11, 1-2-3, Spring 2000.
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LINKS
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FORMULA
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MAPLE
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N:= 1000: # to get all terms <= N
Primes:= select(isprime, {2, seq(i, i=3..floor(N/4))}):
S:= select(`<=`, {seq(p^5, p = Primes), seq(seq(p*q^2, p=Primes minus {q}), q=Primes)}, N):
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MATHEMATICA
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Select[Range[500], DivisorSigma[0, #]==6&] (* Harvey P. Dale, Oct 02 2014 *)
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PROG
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(Python)
from sympy import divisor_count
def ok(n): return divisor_count(n) == 6
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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