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A116565
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Hexagonal numbers whose number of divisors is also a hexagonal number.
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2
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1, 28, 45, 153, 325, 4753, 7381, 29161, 56953, 65341, 73536, 166753, 266085, 270480, 354061, 1062153, 1383616, 3123750, 3525840, 3873936, 5247180, 5649841, 6060421, 6644835, 6835753, 6924781, 7006896, 7870528, 9925740, 10285380, 12708361
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OFFSET
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1,2
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COMMENTS
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The hexagonal numbers are numbers of the form n(2n-1) (A000384).
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LINKS
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EXAMPLE
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45 is in the sequence because 45=5(2*5-1) is a hexagonal number having 6 divisors (1,3,5,9,15,45) and 6=2(2*2-1) is also a hexagonal number.
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MAPLE
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with(numtheory): a:=proc(n) local h: h:=tau(n*(2*n-1)): if type(sqrt(1+8*h)/4+1/4, integer) then n*(2*n-1) else fi end: seq(a(n), n=0..3000); # Emeric Deutsch, Apr 06 2006
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MATHEMATICA
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With[{hex=PolygonalNumber[6, Range[3000]]}, Select[hex, MemberQ[hex, DivisorSigma[0, #]]&]] (* Harvey P. Dale, Mar 10 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006
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EXTENSIONS
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STATUS
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approved
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